Differential Equations of My Young Years PDF
Preview Differential Equations of My Young Years
Vladimir Maz’ya Differential Equations of My Young Years Vladimir Maz’ya Differential Equations of My Young Years VladimirMaz’ya Domherreva¨gen20 Sollentuna Sweden ISBN978-3-319-01808-9 ISBN978-3-319-01809-6(eBook) DOI10.1007/978-3-319-01809-6 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2014933549 ©SpringerInternationalPublishingSwitzerland2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerpts inconnectionwithreviewsorscholarlyanalysisormaterialsuppliedspecificallyforthepurposeofbeing enteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework.Duplication ofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheCopyrightLawofthe Publisher’s location, in its current version, and permission for use must always be obtained from Springer.PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter. ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerBaselispartofSpringerScience+BusinessMedia(www.springer.com) Foreword This autobiographic book by Vladimir Maz’ya, an outstanding mathematician of worldwidereputation,aremarkablerepresentativeoftheSt.Petersburg-Leningrad school of mathematics,1 is intended for a diverse readership that includes people whohavehadlittletodowithmathematics.Forthisreason,whileintroducingthe authorofthebooktothepublic,itisperhapspointlesstodescribeandenumeratehis scientific achievements inanydetail.Iwould simply say thatthe greatnumber of hispublications(about500articlesand20books),2andthegreatdepthoftheresults hehasobtained,hisfundamentalnewideas,andhisskilledtechnique,cannotfailto make a strong impression on a wide variety of readers. This statement is richly confirmedbyaWikipediaarticlethat,inadditiontonamingV.Mazya’sworks,also citeshishonorarytitlesandawardsandtheuniversitieswherehewroteandtaught intheUSSR,WesternEurope,andtheUSA. I am fortunate to have been the coauthor and friend of such a Master – a term used here in the sense of this word as coined by Bulgakov. (Near the end of Maz’ya’s book, see the Sect. 6.13, which touches upon the correlation between Bulgakov’s“master”andMazya’slistsoftitles,diplomas,etc.) Thefactthatmathematicsappearsonmanyofitspagesinnowaydiminishesthe book’sclarityofdiscourseandattractiontoavarietyofreaders.Whileminimizing theuseofspecialtermsandformulations,theauthorshareswiththereaderstories of the dramatic emotions and strains that a mathematician can experience in strugglingwithacomplexprobleminpursuitofa,sometimesseeminglyconstantly escaping,solution.Asanexample,Icitetheauthor’srecountingofhisdiscoveryof anewapproachtothetheoryofSobolevspaces(theSect.5.9)andanunexpected solutionofaproblemfromHilbert’sfamouslist.ButthemathematicsinMaz’ya’s 1SeeV.I.Smirnov’sspeech,quotedintheSect.6.4. 2Amongthemisavoluminousandcaptivatingmonographdevotedtothelifeandworksofthe famous French mathematician J. Hadamard; it is quite accessible to a non-specialist. (Jacques Hadamard, A Universal Mathematician, V. Maz’ya, T. Shaposhnikova, AMS, LMS; there are FrenchandRussiantranslations). v vi Foreword book(asinthelifeofeveryseriousscholar)isnotseparatedfromeverydaylifeor the people around him (both colleagues and non-mathematicians). His personal connections, so vividly expressed by the author, determine a singular, and even somewhatpeculiar,character ofthe bookthatspeakstothe interestsofmathema- ticians as well as to the general public. His abundance of astute observations, concrete depictions, and vivid portraits gives the text an encyclopedic character, andmakesitavaluablesourceofinformationforthehistorianoftheSovietlifein the40s–60softhelastcentury. Subjectsrelatedtomathematicsdonotappearinthebookatonce;indeeditsfirst partiscompletelydevoidofthem.Atthebeginningofthebook,theauthortellsus of his early childhood which coincided with the hard times of the war. All his grandparentsperishedinthesiegeofLeningrad.Hisfatherandtwounclesdiedat thefront.(Onecan’thelpbutrememberSlutsky’spoem:“Thebulletsparedme.So that they may say truly: ‘The Jews did not fight in the war. They all returned safely.’”) Thebookdescribestheauthor’sandhismother’sevacuationtotherearduring thewar,hisschoolyearsinpostwarLeningrad,poverty,andcommunalapartments (alas,astillexistingcharacteristicofSovietlife).Allofthatisvividlydescribedin thefirsthalfofthebook.Here,aswellasinthesecondhalf,therearemanyrealiaof Soviet everyday life requiring words that are (fortunately, given their meanings) disappearing daily. These words may need to be explained even to a present-day Russianreader,tosaynothingofanEnglishspeakerwhowouldmostlikelylackthe necessarycontext.(Irefertosuchtermsas“communalka”(Communalapartment), “kerosinka”(kerosenestove),“fifthitem”(internalpassportrecordofJewishness), “permitted to travel abroad – not permitted to travel abroad” (for political or national reasons), “ideological commission” (it checks your loyalty to Commu- nism)andahostofotherswithdevastatingconnotations. Approximatelyfromthemiddleofthebook,themathematicalcontentincreases and becomes more and more emphasized. The negative features of Soviet reality werehistoricallycombinedwithawell-organizededucationalsystem,atleastinits physicsandmathematicsaspects.WhilereadingV.Maz’ya’sbook,welearnalot ofgoodthingsofthemathematicallifeinLeningrad–aboutschoolchildrenkeen onmathematics,amateurcirclesofyoungmathematicians,contests(Olympiads)in mathematics,andfinallyoftheMathmech(acolloquialnameforMathematicaland Mechanical Department of the Leningrad/St. Petersburg University). There is a galleryofportraits–descriptiveandlovinglyselectedphotographicrepresentations – reminiscent of the mathematicians’ life of that time in Leningrad. It was quite intensive and abundant in both people and events. The beginning student could easily find a knowledgeable professor. Freshmen were taught by venerable math- ematiciansaswellasbypeers.Anditwaspossibletocontactaprofessorinother settingsthaninclass.Anexampleofsuchinformalandtrulycrucialcontactswasa conversationofStudentMaz’yawithProfessorMikhlin(seethe Sect.5.7). In the second part of the book (devoted to the “Mathmech”), a peculiarity mentioned above becomes clearly apparent. Episodes of the author’s creative activity, reconnaissance of his own path in science, work with mathematical Foreword vii problemsandflashesofinspiration,allofthesealternatewithstoriesofeventsand meetingsofnon-mathematicallife.ThedescriptionofMaz’ya’sdiscoveryofanew approachtoSobolevspacestheorygivesplacetoachapterconcernedwithatripto the Virgin Soil. After two dissertation defenses – the Candidate and Doctor of Sciences degrees – the story passes on to the so-called special stores and to the banishment of most travel abroad. A significant amount of space is dedicated to meetingswithactors,musicians,andimpressionsoftheirworks. Ihavebrieflyandonlypartiallymentionedwhatispresentedinthebook.Ihope otherreaderswillexperience thesame enjoymentthatImyselfhave had.Iwould alsoliketoaddresstheauthorwithawish(thatprobablywouldbejoinedbyother readers):Pleasewriteasequel.Itwouldnodoubtbesomewhatmoremathematical, butwouldstillbeappreciatedbybothmathematiciansandthegeneralpublic. V.P.Havin MeritoriousScientistofRussianFederation ThiSisaFMBlankPage Author’s Notes Iwrotethisbookattheinsistenceofmychildren.Thetextcoverseventsfrom1937 till1968only. Withtheadvancementoftimeasmylifewenton,itbecamenecessarytospeak moreandmoreofmathematics,whichformanyyearsfortunatelyremainedandstill remains the core of my existence. But because any description of this material cannot be fully understood by non-specialists, it was doomed to failure a priori. This is actually the main reason why my memoirs had to be stopped at quite an earlydate. MypleasanttasknowistoexpresscordialthankstomywifeTanya,mychildren Misha and Gali-Dana, my son-in-law Nekod as well as the friends of my youth Leonid Druz and Arkady Alexeev. All of them were of great help in writing this book.IwouldliketoextendmyheartfeltgratitudetoVictorHavinforaddingthe Foreword to the English edition. I also owe special thanks to Arkady Alexeev for takingtheburdenoftranslatingthetextoftheRussianoriginalwithitscomplicated terminologyandmanyidioms. I would ask Sylvia Lotrovsky and Thomas Hempfling of Springer Basel to acceptmygratitudefordecidingtopublishmyreminiscencesinEnglish. ix
The list of books you might like
