Hölder continuity of weak solutions to subelliptic equations with rough coefficients / Eric T. Sawyer, Richard L. Wheeden.

Format:

Book

Author/Creator:

Sawyer, E. T. (Eric T.), 1951- author.

Wheeden, Richard L., author.

Series:

Memoirs of the American Mathematical Society ; no. 847.

Memoirs of the American Mathematical Society, 0065-9266 ; number 847

Language:

English

Subjects (All):

Differential equations, Partial--Numerical solutions.

Differential equations, Partial.

Differential equations, Hypoelliptic--Numerical solutions.

Differential equations, Hypoelliptic.

Physical Description:

1 online resource (176 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2006]

Language Note:

English

Summary:

This mathematical monograph is a study of interior regularity of weak solutions of second order linear divergence form equations with degenerate ellipticity and rough coefficients. The authors show that solutions of large classes of subelliptic equations with bounded measurable coefficients are H lder continuous. They present two types of results f

Contents:

Intro

Contents

Overview

Chapter 1. Introduction

1. An extension of the Fefferman-Phong theorem to rough operators

2. Extensions of Hormander's theorem to rough operators

3. Applications to quasilinear equations

Chapter 2. Comparisons of conditions

1. Flags and commutators

2. Homogeneous and prehomogeneous spaces

3. Comparability with the subunit balls

Chapter 3. Proof of the general subellipticity theorem

1. W-weak solutions and admissible compositions

2. Weak reverse Hölder inequalities and Moser iteration

3. The strong Harnack inequality

4. Hölder continuity of solutions

Chapter 4. Reduction of the proofs of the rough diagonal extensions of Hörmander's theorem

1. Accumulating sequences of Lipschitz cutoff functions in annuli

2. The axiom

3. The Sobolev and Poincaré inequalities

4. Adapted vector fields and prehomogeneous spaces

5. The reduction of the proofs

Chapter 5. Homogeneous spaces and subrepresentation inequalities

1. The noninterference balls

2. The flag balls

Chapter 6. Appendix

1. Necessity of the Fefferman-Phong condition

2. Necessity of the Sobolev and Poincaré inequalities

3. The noninterference balls A (x,r) and the reverse Hölder condition

4. Reverse Hölder examples

5. Product reverse Hölder

6. The noninterference conditions

7. Other notions of weak solution

8. Alternate methods of proof

Bibliography

Glossary of Terms and Symbols

A

B

C

D

E

F

G

H

I

L

M

N

P

Q

R

S

T

U

V

W.

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 153-154).

Description based on print version record.

ISBN:

1-4704-0451-6