# 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

### Table of Contents

**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