# Lectures on Elliptic and Parabolic Equations in Sobolev Spaces

### About this Title

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

Publication: Graduate Studies in Mathematics

Publication Year
2008: Volume 96

ISBNs: 978-0-8218-4684-1 (print); 978-1-4704-2121-2 (online)

DOI: http://dx.doi.org/10.1090/gsm/096

MathSciNet review: MR2435520

MSC: Primary 35-01; Secondary 35J15, 35K10, 35S05, 46E35, 46N20

### Table of Contents

**Front/Back Matter**

**Chapters**

- Chapter 1. Second-order elliptic equations in $W^{2}_{2}(\mathbb {R}^{d})$
- Chapter 2. Second-order parabolic equations in $W^{1,k}_{2}(\mathbb {R}^{d+1})$
- Chapter 3. Some tools from real analysis
- Chapter 4. Basic $\mathcal {L}_{p}$-estimates for parabolic and elliptic equations
- Chapter 5. Parabolic and elliptic equations in $W^{1,k}_{p}$ and $W^{k}_{p}$
- Chapter 6. Equations with VMO coefficients
- Chapter 7. Parabolic equations with VMO coefficients in spaces with mixed norms
- Chapter 8. Second-order elliptic equations in $W^{2}_{p}(\Omega )$
- Chapter 9. Second-order elliptic equations in $W^{k}_{p}(\Omega )$
- Chapter 10. Sobolev embedding theorems for $W^{k}_{p}(\Omega )$
- Chapter 11. Second-order elliptic equations $Lu-\lambda u=f$ with $\lambda $ small
- Chapter 12. Fourier transform and elliptic operators
- Chapter 13. Elliptic operators and the spaces $H^{\gamma }_{p}$