LEADER 05372nam 2200757 450 001 9910467573503321 005 20210430202756.0 010 $a3-11-033224-8 010 $a3-11-039008-6 024 7 $a10.1515/9783110332247 035 $a(CKB)4230000000000189 035 $a(EBL)4459580 035 $a(SSID)ssj0001635073 035 $a(PQKBManifestationID)16388553 035 $a(PQKBTitleCode)TC0001635073 035 $a(PQKBWorkID)14909530 035 $a(PQKB)11366754 035 $a(PQKBManifestationID)16331766 035 $a(PQKBWorkID)14910021 035 $a(PQKB)24642701 035 $a(MiAaPQ)EBC4459580 035 $a(DE-B1597)213037 035 $a(OCoLC)939911315 035 $a(OCoLC)951149174 035 $a(DE-B1597)9783110332247 035 $a(Au-PeEL)EBL4459580 035 $a(CaPaEBR)ebr11177581 035 $a(CaONFJC)MIL908133 035 $a(OCoLC)945874272 035 $a(EXLCZ)994230000000000189 100 $a20160415h20162016 uy 0 101 0 $aeng 135 $aur|nu---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aSingular solutions of nonlinear elliptic and parabolic equations /$fAlexander A. Kovalevsky, Igor I. Skrypnik, Andrey E. Shishkov 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cde Gruyter,$d2016. 210 4$dİ2016 215 $a1 online resource (448 p.) 225 1 $aDe Gruyter Series in Nonlinear Analysis and Applications,$x0941-813X ;$vVolume 24 300 $aDescription based upon print version of record. 311 $a3-11-031548-3 311 $a3-11-033225-6 320 $aIncludes bibliographical references. 327 $tFront matter --$tForeword --$tContents --$tPart I. Nonlinear elliptic equations with L1-data --$tChapter 1. Nonlinear elliptic equations of the second order with L1-data --$tChapter 2. Nonlinear equations of the fourth order with strengthened coercivity and L1-data --$tPart II. Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order --$tChapter 3. Removability of singularities of the solutions of quasilinear elliptic equations --$tChapter 4. Removability of singularities of the solutions of quasilinear parabolic equations --$tChapter 5. Quasilinear elliptic equations with coefficients from the Kato class --$tPart III. Boundary regimes with peaking for quasilinear parabolic equations --$tChapter 6. Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations --$tChapter 7. Method of functional inequalities in peaking regimes for parabolic equations of higher orders --$tChapter 8. Nonlocalized regimes with singular peaking --$tChapter 9. Appendix: Formulations and proofs of the auxiliary results --$tBibliography --$tBack matter 330 $aThis monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form. The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis. Contents: Foreword Part I: Nonlinear elliptic equations with L^1-dataNonlinear elliptic equations of the second order with L^1-dataNonlinear equations of the fourth order with strengthened coercivity and L^1-dataPart II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography 410 0$aDe Gruyter series in nonlinear analysis and applications ;$vVolume 24. 606 $aDifferential equations, Elliptic 606 $aDifferential equations, Nonlinear 606 $aDifferential equations, Parabolic 608 $aElectronic books. 615 0$aDifferential equations, Elliptic. 615 0$aDifferential equations, Nonlinear. 615 0$aDifferential equations, Parabolic. 676 $a515/.3534 700 $aKovalevsky$b Alexander A.$01048191 702 $aSkrypnik$b Igor I. 702 $aShishkov$b Andrey E. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910467573503321 996 $aSingular solutions of nonlinear elliptic and parabolic equations$92476313 997 $aUNINA