Higher integrability in the obstacle problem for the fast diffusion equation

Abstract

We prove local higher integrability of the spatial gradient for solutions to obstacle problems of porous medium type in the fast diffusion case $m<1$. The result holds for the natural range of exponents that is known from other regularity results for porous medium type equations. We also cover the case of signed solutions.

References in corpus (5)

• Higher integrability for doubly nonlinear parabolic systems
• Self-improving property of degenerate parabolic equations of porous medium-type
• Self-improving property of the fast diffusion equation
• A reverse Hölder inequality for the gradient of solutions to Trudinger's equation
• Higher integrability for obstacle problem related to the singular porous medium equation