Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations

N. V. Krylov, University of Minnesota, Minneapolis, MN.

• 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