Regularity of solutions to degenerate normalized $p$-Laplacian equation with general variable exponents

Abstract

In this paper, we consider a kind of degenerate normalized $p$-Laplacian equation with general variable exponents. We establish local $C^{1,{\alpha }^{\prime }}$ regularity of viscosity solutions by making use of the compactness argument, scaling techniques and the localized oscillating method. In addition, we also obtain almost optimal pointwise $C^{1,\tau }$ regularity for degenerate free transmission problem related to normalized $p$-Laplacian. Our argument is based on a new improved oscillation-type estimate combined with a localized analysis.

arXiv comment34 pages, Referees' suggestions incorporated, To appear in Potential Anal

References in corpus (3)

• $C^{1,\alpha }$ regularity of solutions of degenerate fully non-linear elliptic equations
• A proof of the $C^{p^{\prime }}$-regularity conjecture in the plane
• Estimates on elliptic equations that hold only where the gradient is large

Cited by in corpus (1)

• Regularity of solutions for degenerate or singular fully nonlinear integro-differential equations