Non-linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis: The Helge Holden Anniversary Volume PDF
Preview Non-linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis: The Helge Holden Anniversary Volume
Series of Congress Reports NF MN S e r i e s o f C o n g r e s s R e p o r t s ir lsit ao Hz tn eG h- nes eL rikzt min e Rs ae y is, ta Non-Linear Partial eH ir Non-Linear Partial Differential ba c rr aP oa la Equations, Mathematical Physics, and ald Pr Differential Equations, nd H ht Stochastic Analysis a i K ya n The Helge Holden Anniversary Volume risch sil D Mathematical Physics, te c ia-O si Fritz Gesztesy, Harald Hanche-Olsen, Espen R. Jakobsen, n Slse , affe and Stochastic Analysis e Yurii Lyubarskii, Nils Henrik Risebro and Kristian Seip, in nr Editors p, E, Es d en dp St The Helge Holden Anniversary Volume iten ti o oa TIth cios lvleoclutsm ceo nist rdiebduitcioatnesd b tyo nHuemlgeer oHuosl dsecnie onnti sthtse wocitcha seixopne ortfi sheis i n6 0ntohn a-lninnievaerr spaarryt.i al rsR. J chl E differential equations (PDEs), mathematical physics, and stochastic analysis, a aq k Fritz Gesztesy reflecting to a large degree Helge Holden’s longstanding research interests. o su b t Accordingly, the problems addressed in the contributions deal with a large range of s ia Harald Hanche-Olsen topics, including, in particular, infinite-dimensional analysis, linear and nonlinear e ct n i PDEs, stochastic analysis, spectral theory, completely integrable systems, random , Ao matrix theory, and chaotic dynamics and sestina poetry. They represent to some extent Yu nn Espen R. Jakobsen the lectures presented at the conference Non-linear PDEs, Mathematical Physics and r as Stochastic Analysis, held at NTNU, Trondheim, July 4–7, 2016. ii L ly, Yurii Lyubarskii y s The mathematical tools involved draw from a wide variety of techniques in functional u Nils Henrik Risebro i analysis, operator theory, and probability theory. b s a r Kristian Seip s This collection of research papers will be of interest to any active scientist working in k one of the above mentioned areas. ii , Editors ISBN 978-3-03719-186-6 www.ems-ph.org SCR Gesztesy et al. | Egyptienne F | Pantone 116, 287 | RB 33 mm EMS Series of Congress Reports EMS Congress Reports publishes volumes originating from conferences or seminars focusing on any field of pure or applied mathematics. The individual volumes include an introduction into their subject and review of the contributions in this context. Articles are required to undergo a refereeing process and are accepted only if they contain a survey or significant results not published elsewhere in the literature. Previously published: Trends in Representation Theory of Algebras and Related Topics, Andrzej Skowron´ski (ed.) K-Theory and Noncommutative Geometry, Guillermo Cortiñas et al. (eds.) Classification of Algebraic Varieties, Carel Faber, Gerard van der Geer and Eduard Looijenga (eds.) Surveys in Stochastic Processes, Jochen Blath, Peter Imkeller and Sylvie Rœlly (eds.) Representations of Algebras and Related Topics, Andrzej Skowron´ski and Kunio Yamagata (eds.) Contributions to Algebraic Geometry. Impanga Lecture Notes, Piotr Pragacz (ed.) Geometry and Arithmetic, Carel Faber, Gavril Farkas and Robin de Jong (eds.) Derived Categories in Algebraic Geometry. Toyko 2011, Yujiro Kawamata (ed.) Advances in Representation Theory of Algebras, David J. Benson, Henning Krause and Andrzej Skowron´ski (eds.) Valuation Theory in Interaction, Antonio Campillo, Franz-Viktor Kuhlmann and Bernard Teissier (eds.) Representation Theory – Current Trends and Perspectives, Henning Krause, Peter Littelmann, Gunter Malle, Karl-Hermann Neeb and Christoph Schweigert (eds.) Functional Analysis and Operator Theory for Quantum Physics. The Pavel Exner Anniversary Volume, Jaroslav Dittrich, Hynek Kovarˇík and Ari Laptev (eds.) Schubert Varieties, Equivariant Cohomology and Characteristic Classes, Jarosław Buczyn´ski, Mateusz Michałek and Elisa Postinghel (eds.) Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis The Helge Holden Anniversary Volume Fritz Gesztesy Harald Hanche-Olsen Espen R. Jakobsen Yurii Lyubarskii Nils Henrik Risebro Kristian Seip Editors Editors: Fritz Gesztesy Harald Hanche-Olsen Department of Mathematics Espen R. Jakobsen Baylor University Yurii Lyubarskii Sid Richardson 305I, One Bear Place #97328 Kristian Seip Waco, TX 76798-7328 Department of Mathematical Sciences USA Norwegian University of Science and Technology Alfred Getz vei 1 Email: [email protected] 7491 Trondheim Norway Nils Henrik Risebro Department of Mathematics Email: h [email protected] University of Oslo [email protected] P.O. Box 1036, Blindern [email protected] N-0316 Oslo [email protected] Norway Email: [email protected] 2010 Mathematics Subject Classification: Primary: 15B52, 35J10, 35L65, 35Q41, 35Q51, 35Q53, 37K10, 42B20, 46N20, 46N30, 46T12, 47B36, 47F05, 60H20, 68N30, 76S05; secondary: 33C45, 35A01, 35A02, 35L80, 37D45, 39A12, 47A10, 47N20, 47N30, 60B20. Key words: Infinite-dimensional analysis, partial differential equations, hyperbolic conservation laws, stochastic analysis, spectral theory, discrete evolution, completely integrable systems, random matrix theory, chaotic dynamics. ISBN 978-3-03719-186-6 The Swiss National Library lists this publication in The Swiss Book, the Swiss national bibliography, and the detailed bibliographic data are available on the Internet at http://www.helveticat.ch. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © European Mathematical Society 2018 Contact address: European Mathematical Society Publishing House Seminar for Applied Mathematics ETH-Zentrum SEW A21 CH-8092 Zürich, Switzerland Phone: +41 (0)44 632 34 36 Email: [email protected] Homepage: www.ems-ph.org Typeset by the editors using the authors’ TeX files: Harald Hanche-Olsen, Trondheim, Norway Printing and binding: Beltz Bad Langensalza GmbH, Bad Langensalza, Germany ∞ Printed on acid free paper 9 8 7 6 5 4 3 2 1 Preface ThisFestschriftisdedicatedtoHelgeHolden ontheoccasionof his60thbirthday. HelgeHoldenwasborntoparentsFinnHolden(1928–),atextbookauthor,histo- rian,andhighschoolteacher,andKirstenneeWolfhagen(1931–1999),alibrarian andpsychologist,onSeptember28,1956,inOslo,Norway. Helgegrewupwith twoyoungerbrothers,Steinar,whoisprofessorofeconomicsattheUniversityof Oslo,andLars,whoisManagingDirectorattheNorwegianComputingCenterin Oslo. Interestingly,Helgehasajointpaper[58]1withhistwobrothers. Helgedecidedearlytostudymathematicsandphysics,andafterservingthe mandatoryoneyearmilitaryservice,heenteredtheUniversityof Osloin1976. Inthefallof 1980hestartedtoworkonhiscand.real. thesiswiththelateProf. Raphael Høegh-Krohn (1938–1988) as advisor, working on solvable models in non-relativisticquantummechanics. Inthefallof 1981hegraduatedwiththe cand.real. exam,hisgradesbeingsoimpressivethattheresultwasreportedtothe KingofNorwayintheCouncilofState. RaphaelHøegh-Krohn–acharismaticandbrilliantmathematicalphysicist attheUniversityofOslo–broughtHelgeincontactwiththegrouparoundProf. Sergio Albeverio in Bochum, and the young mathematicians Fabio Martinelli, Werner Kirsch, and, Fritz Gesztesy. Fritz came to Oslo because he had found an improvement in an important paper by Raphael and Sergio (marking the beginningofanintensivecollaborationwithbothofthem),andatthatoccasion FritzandHelgealsostartedworkingtogether,andhavecontinuedtodosoever since. Inthosedays,theworkcenteredaroundso-calledpointinteractionmodels innonrelativisticquantummechanics,andresultedinthebookβ[1],publishedby Springerin1988,translatedintoRussian,andre-issuedina2ndeditionbythe AmericanMathematicalSocietywithanappendixbyProf.PavelExnerin2005. Ithasestablisheditselfasthestandardreferenceinthefield,anditisfrequently citedinboththephysicsandmathematicsliterature. Intheearly1980s,Norwaywasgoingthroughrapidanddramaticdevelopment. AtChristmasof1969,thefirstoilwasdiscoveredintheNorthSea–theEkofiskfield –stilloneofthelargestintheNorthSea. Thequestionwashowtotakeadvantage 1Numbersrefertothecompletelistofpublications. vi Preface ofthistothebenefitofNorwegiansociety. Fortunately,thegovernmentdecidedto buildupnationalcompetencyinNorway,resultinginadramaticimprovementin thestandardoflivinginNorway. ThosewhovisitedNorwayintheearly’80sand visitnow,willseeanextrememakeoverinNorway–itsimplyisadifferentcountry now. In the early ’80s, the Norwegian oil companies Saga, Hydro, and Statoil neededscientistswithagoodbackgroundinthesciencesandinmathematics,and thecompaniessupportedmathematicalresearch. RaphaelandHelge,together withNilsHenrikRisebro,LarsHolden,ToreGimse,KyrreandFrodeBratvedt, andChristianBuchholz,embarkedontheprojecttodevelopafullscalepetroleum reservoirsimulator. Theapproachwasbasedatfirstonlotsof enthusiasmand, retrospectively,lessondeepknowledgeof reservoirsimulation;itwasalsothe startofalife-longcollaborationbetweenHelgeandNilsHenrik. Unfortunately, Raphaelsuddenlypassedawayin1988,andHelgetookoverasPhDadvisorof NilsHenrikandLars. Thedevelopmentofthereservoirsimulatorsubsequently changedfocus,butitistothisdaystillusedbySchlumberger–theworld’sleading oilfieldservicescompany. Atthistimetherewasessentiallynoactivityinpartialdifferentialequations inNorway. TogetherwithProf.RagnarWintherinOslo,HelgeandRagnarhave, togetherwiththeirsubstantialnumberof students,beeninstrumentalindevel- opingthefieldofpartialdifferentialequationsintooneofthestrongestareasof Norwegianmathematics. Theresearchisnolongerrestrictedtotopicsrelevantto flowinporousmedia,andaspecialfocushasbeentounderstandtheinteraction between theoretical results and numerical simulations. There are now strong researchgroupsinpartialdifferentialequationsattheuniversitiesinOslo,Bergen, andTrondheim,inadditiontothatatSINTEF. AftercompletionofhisPhD,Helgewentfortheacademicyear1985–86tothe CourantInstituteofMathematicalSciencesofNewYorkUniversityonaFulbright scholarshiptojointhegroupofProf.JamesGlimm. Whilethere,hewasoffereda permanentpositionattheNorwegianInstituteofTechnology(nowNTNU–the NorwegianUniversityofScienceandTechnology),inTrondheim,Norway,and hehasremainedatNTNUeversince. Hespentthespringsemester1989atthe CaliforniaInstituteofTechnology,withProf. BarrySimon,andtheacademicyear 1996/97attheUniversityofMissouri,Columbia,withFritz. Helge’smathematicalactivityspansseveralareas. Startingoutinmathemati- calphysics,focusingonnonrelativisticquantummechanics,helaterturnedhis interesttononlinearpartialdifferentialequations. Heretheinterestinitiallywas concentratedonthestudyofflowofhydrocarbonsinporousmedia,andthemost importantmathematicalresultscameinthetheoryofhyperbolicconservations laws,where,togetherwithNilsHenrik,hewrotethebookβ[4]thatrepresents thestandardpresentationof theso-calledfront-trackingapproachtohyperbolic Preface vii conservationlaws. Withthegroupof Prof.BerntØksendalinOslo,Helgeworked onstochasticdifferentialequationsusingtheso-calledwhitenoiseapproach,and theirresultswerepresentedinthebookβ[2]. WithFritz,Helge’sinterestturnedto completelyintegrablesystems–wherethecelebratedKdVequationisoneof the mostrecognizedexamples–andtheycollectedtheirresultsinthetwo-volume treatiseβ[5,6],thesecondvolumewrittenjointlywithJohannaMichorandGerald Teschl. Subsequently, Helge’s interest moved to the Camassa–Holm equation, whichhehadalreadystudiedwithFritzinthealgebro-geometricsetting. Nowthe problemturnedintothestudyofanevolutionequationwhosesolutionsencounter wavebreaking,andthisstudyledtofurtherworkalsoonthenonlinearvariational waveequation. InthisareaheworkedwithXavierRaynaudandKatrinGrunert. Hismostrecentbookdiscussesso-calledoperatorsplittingmethodsfornonlinear partialdifferentialequationswithroughsolutions,andisjointwithKnut-Andreas Lie,KennethH.Karlsen,andNilsHenrikβ[7]. Acommonfeatureofallofhisworkisthedeepinteractionbetweenmathe- maticsandphysics. Todate,hehasco-authoredwellover160publicationsand 7books(4of whicharealreadyin2ndedition,ararefeat). Helgetrulyenjoys collaborationandtothisdayhasworkedwithwellover60collaborators. Hiswork hasbeenextensivelycited,accordingtoMathSciNet,almost2491timesbymore than1631researchers.2 Helgehasreceivednumeroushonors,amongwhichwementionthefollowing: –ElectiontotheNorwegianAcademyofScienceandLetters –ElectiontotheRoyalNorwegianSocietyofSciencesandLetters –ElectiontotheNorwegianAcademyofTechnologicalSciences –ElectiontotheEuropeanAcademyofSciences –Fellow,AmericanMathematicalSociety –Fellow,SocietyforIndustrialandAppliedMathematics(SIAM) –HegaveaninvitedtalkattheEuropeanCongressofMathematicsinStockholm in2004. AtNTNUHelgehasbeeninvolvedinseveralactivities–hehashadastaggering numberof almost90masterstudentsand24PhDstudents(3currently),most of whom are active researchers with successful careers of their own, and he is currently serving on the Board of NTNU. In 1993 he took the initiative to organizeanannualLarsOnsagerLectureandLarsOnsagerProfessorshipatNTNU tocommemoratetheiconicLarsOnsager(1903–76),NobelLaureateinChemistry in1967,whoseAlmaMaterwastheNorwegianInstituteofTechnology;25years laterthisactivityisstillgoingstrong. 2MathSciNet,April1,2017.No,notanAprilfoolsjoke! viii Preface Historically, NTNU has had a strong focus on engineering with a constant sourceofexcellentstudentscomingfromtheprograminIndustrialMathematics, developedtogetherwithpartnersinECMI–EuropeanConsortiumofMathematics inIndustry. HelgegotinvolvedwiththisactivitythroughthelateProf.Henrik Martens(1927–93)atNTNU,whowasoneofthefoundersofECMI.Helgeserved asPresidentofECMIduringtheperiod2004–06. Onthenationalscene,Helgehasbeenexceptionallyactive. Hechairedseveral key panels of the Research Council of Norway for extended periods, the most importantbeingthepanelthatdecidedonallnationalindividualresearchgrants inmathematicsandthenaturalsciences. IntheScandinaviancountries,Helge has chaired evaluations of research and education in mathematics at several universitiesinDenmarkandSweden. Similarly,ontheEuropeanscene,Helgehas chairedthepanelof theEuropeanResearchCouncilthatawardstheprestigious ConsolidatorGrantsinMathematics. HelgehaswrittennumerousarticlesinNorwegiannewspapersandjournals onvariousresearchpoliticaltopicsandthepopularizationofmathematics. Hehas beenveryactivelyinvolvedintheAbelPrizeinMathematicssinceitsstartin2003. Inparticular,heservedasChairoftheAbelBoardoftheNorwegianAcademyof ScienceandLetters,fortheperiodof2010–14. Duringhischairmanshipseveral novelactivitiesstarted,forinstance,thecompetitionUngeAbel,theHeidelberg LaureateForum,andthecollaborationwith PetroleumGeo-Services. Healsotook theinitiativetoeditbooksabouttheAbelLaureates,andwithRagniPienetwo volumeshavebeencompletedε[7,12],withathirdvolumecurrentlyinpreparation. Helgehasalwaysbeenastrongproponentof internationalcollaboration,and heservedasSecretary(2003–06)andVicePresident(2007–10)of theEuropean MathematicalSociety. CurrentlyheisservingasSecretaryof theInternational MathematicalUnion(IMU),withheadquartersinBerlin,Germany. He has served on the Board of the Norwegian Academy of Technological SciencesandtheRoyalNorwegianSocietyofSciencesandLetters,andduringthe period2014–16heservedasPresidentofthelatter. WhilethishintsatsomeaccountofHelgeasthescientistandhissubstantial servicetoourprofessioninthenationalaswellasinternationalarena,wewould beamissnottocommentonsomepersonalaspectsof ourlongstandingfriend- shipwithhim. Hiskind,yetfirm,demeanor,hisintegrityandsenseoffairness, hisdedicationtoscience, hisintellectualcuriosityabouttheworldasawhole, substantiallytranscendingthenaturalsciences,hisdeepinterestinthearts,and especially,hisloveofliterature,showshimtobethecomplexandmulti-faceted personalityweallcametoappreciatesomuchovertheyears. Severaloftheeditors arecollaboratorsofHelge’s,someforupto35yearsnow,allofusviewhimasa dearandtrustedfriend. Preface ix The volume at hand is based to some extent on the conference, Non-linear PDEs,MathematicalPhysicsandStochasticAnalysis,heldatNTNU,Trondheim, July4–7,2016(https://wiki.math.ntnu.no/holden60). Thefieldsrepresentedin the contributions to this volume reflect to a large degree Helge’s longstanding researchinterests. Theycenteraroundinfinite-dimensionalanalysis(integralsof probabilisticandoscillatorytype),linearandnonlinearpartialdifferentialequa- tions(includingdiscreteevolutionequations,Ostrovsky–Hunter-typeequations, modelingcrowddynamics,porousmediumtypeequations,nonlineardegener- ateanisotropichyperbolic-parabolicequations,Riemannproblemsformodelsof polymerflooding,systemsofconservationlaws,nonlineardispersivePDEs,com- pensatedcompactnessandisometricimmersionsofmanifolds),stochasticanalysis (optimalcontrolforasystemof stochasticVolterraequations), spectraltheory (includingspectraofleakysurfaces,Hardy–Rellich-typeinequalities,dispersion estimateforone-dimensionalSchrödingeroperators,Schrödingeroperatorsin- volvingtheHeisenbergsub-Laplacian),completelyintegrablesystems(including themodifiedtwo-componentCamassa–Holmsystem),randommatrixtheory,and chaoticdynamicsandsestinapoetry. Finally,weexpressoursinceregratitudetothestaffattheEMS,particularly, Thomas Hintermann, for their help, support, and expertise in producing this volume. Wealsothankallauthorsfortheircontributionsandtherefereesfortheir invaluableassistance. HappyBirthday,Helge,wehopethisvolumebringssomefondmemoriesandjoy! FritzGesztesy HaraldHanche-Olsen EspenR.Jacobsen YuriiLyubarskii NilsHenrikRisebro KristianSeip
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