Description

Book Synopsis
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 classes, or for viscosity solutions. Most of the auxiliary results are taken from old sources, and the main results were obtained in the last few years.

Table of Contents
  • Bellman's equations with constant ``coefficients'' in the whole space
  • Estimates in $L_p$ for solutions of the Monge-Ampere type equations
  • The Aleksandrov estimates
  • First results for fully nonlinear equations
  • Finite-difference equations of elliptic type
  • Elliptic differential equations of cut-off type
  • Finite-difference equations of parabolic type
  • Parabolic differential equations of cut-off type
  • A priori estimates in $C^\alpha$ for solutions of linear and nonlinear equations
  • Solvability in $W^2_{p,\mathrm{loc}}$ of fully nonlinear elliptic equations
  • Nonlinear 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 equations
  • Elements of the $C^{2+\alpha}$-theory of fully nonlinear elliptic and parabolic equations
  • Nonlinear 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 coefficients
  • Uniqueness and existence of extremal viscosity solutions for parabolic equations
  • Appendix A. Proof of Theorem 6.2.1
  • Appendix B. Proof of Lemma 9.2.6
  • Appendix C. Some tools from real analysis
  • Bibliography
  • Index

    Sobolev and Viscosity Solutions for Fully

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      Order before 4pm today for delivery by Wed 24 Jun 2026.

      A Hardback by N.v. Krylov

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        View other formats and editions of Sobolev and Viscosity Solutions for Fully by N.v. Krylov

        Publisher: MP-AMM American Mathematical
        Publication Date: 9/30/2018 12:00:00 AM
        ISBN13: 9781470447403, 978-1470447403
        ISBN10: 1470447401

        Description

        Book Synopsis
        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 classes, or for viscosity solutions. Most of the auxiliary results are taken from old sources, and the main results were obtained in the last few years.

        Table of Contents
        • Bellman's equations with constant ``coefficients'' in the whole space
        • Estimates in $L_p$ for solutions of the Monge-Ampere type equations
        • The Aleksandrov estimates
        • First results for fully nonlinear equations
        • Finite-difference equations of elliptic type
        • Elliptic differential equations of cut-off type
        • Finite-difference equations of parabolic type
        • Parabolic differential equations of cut-off type
        • A priori estimates in $C^\alpha$ for solutions of linear and nonlinear equations
        • Solvability in $W^2_{p,\mathrm{loc}}$ of fully nonlinear elliptic equations
        • Nonlinear 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 equations
        • Elements of the $C^{2+\alpha}$-theory of fully nonlinear elliptic and parabolic equations
        • Nonlinear 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 coefficients
        • Uniqueness and existence of extremal viscosity solutions for parabolic equations
        • Appendix A. Proof of Theorem 6.2.1
        • Appendix B. Proof of Lemma 9.2.6
        • Appendix C. Some tools from real analysis
        • Bibliography
        • Index

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