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Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations
About this Title
N. V. Krylov, University of Minnesota, Minneapolis, MN
Publication: Mathematical Surveys and Monographs
Publication Year:
2018; Volume 233
ISBNs: 978-1-4704-4740-3 (print); 978-1-4704-4853-0 (online)
DOI: https://doi.org/10.1090/surv/233
MathSciNet review: MR3837125
MSC: Primary 35-02
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Front/Back Matter
Chapters
- Bellman’s equations with constant “coefficients” in the whole space
- Estimates in $L_p$ for solutions of the Monge-Ampère 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 $W^2_{p,loc}$ of fully nonlinear elliptic equations
- Nonlinear elliptic equations in $C^{2+\alpha }_{loc(\Omega )\cap C(\bar \Omega )}$
- Solvability in $W^{1,2}_{p,loc}$ 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
- Proof of Theorem 6.2.1
- Proof of Lemma 9.2.6
- Some tools from real analysis
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