Differential and Integral Equations

On the higher integrability for certain nonlinear problems

Abstract

We prove local higher integrability for gradients of solutions to a large class of elliptic equations of the type $\text{div} A(x,\nabla u) = 0$ by studying the deviation, in a suitable sense, of the operator $A$ to be constant with respect to $x.$

Article information

Source
Differential Integral Equations, Volume 21, Number 3-4 (2008), 247-263.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356038779

Mathematical Reviews number (MathSciNet)
MR2484008

Zentralblatt MATH identifier
1224.35128

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B65: Smoothness and regularity of solutions

Citation

Verde, Anna; Zecca, Gabriella. On the higher integrability for certain nonlinear problems. Differential Integral Equations 21 (2008), no. 3-4, 247--263. https://projecteuclid.org/euclid.die/1356038779