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Sobolev and viscosity solutions for fully nonlinear elliptic and parabolic equations

Author: N V Krylov
Publisher: Providence, Rhode Island : American Mathematical Society, [2018] ©2018
Series: Mathematical surveys and monographs, no. 233.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov-Safonov and the Evans-Krylov theorems, are taken from old sources,  Read more...
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Document Type: Book
All Authors / Contributors: N V Krylov
ISBN: 9781470447403 1470447401
OCLC Number: 1039672482
Notes: "Applied mathematics"--Cover.
Description: xiv, 441 pages ; 27 cm.
Contents: Bellman's equations with constant ``coefficients'' in the whole spaceEstimates in $L_p$ for solutions of the Monge-Ampere type equationsThe Aleksandrov estimatesFirst results for fully nonlinear equationsFinite-difference equations of elliptic typeElliptic differential equations of cut-off typeFinite-difference equations of parabolic typeParabolic differential equations of cut-off typeA priori estimates in $C^\alpha$ for solutions of linear and nonlinear equationsSolvability in $W^2_{p,\mathrm{loc}}$ of fully nonlinear elliptic equationsNonlinear elliptic equations in $C^{2+\alpha}_{\mathrm{loc}}(\Omega)\cap C(\overline{\Omega})$Solvability in $W^{1,2}_{p,\mathrm{loc}}$ of fully nonlinear parabolic equationsElements of the $C^{2+\alpha}$-theory of fully nonlinear elliptic and parabolic equationsNonlinear elliptic equations in $W^2_p(\Omega)$Nonlinear parabolic equations in $W^{1,2}_p$$C^{1+\alpha}$-regularity of viscosity solutions of general parabolic equations$C^{1+\alpha}$-regularity of $L_p$-viscosity solutions of the Isaacs parabolic equations with almost VMO coefficientsUniqueness and existence of extremal viscosity solutions for parabolic equationsAppendix A. Proof of Theorem 6.2.1Appendix B. Proof of Lemma 9.2.6Appendix C. Some tools from real analysisBibliographyIndex
Series Title: Mathematical surveys and monographs, no. 233.
Responsibility: N.V. Krylov.

Abstract:

Concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. The authors look for solutions in Sobolev  Read more...

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