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E-grāmata: Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations

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Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic EquationsPalielināt
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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, and the main results were obtained in the last few years.

Presentation of these results is based on a generalization of the Fefferman-Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called ``ersatz'' existence theorems, saying that one can slightly modify ``any'' equation and get a ``cut-off'' equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.
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
N. V. Krylov, University of Minnesota, Minneapolis, MN.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97814704485302e.html
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