Riesz potentials and nonlinear parabolic equations

Abstract

The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation. Heat kernels type estimates persist in the nonlinear case

Cited by in corpus (8)

• Self-improving property of degenerate parabolic equations of porous medium-type
• Regularity estimates for singular parabolic measure data problems with sharp growth
• Global regularity for degenerate/singular parabolic equations involving measure data
• Marcinkiewicz regularity for singular parabolic $p$-Laplace type equations with measure data
• Unbounded Supersolutions of Some Quasilinear Parabolic Equations: a Dichotomy
• Shadows of infinities
• Borderline gradient continuity of minima
• Parabolic weighted Sobolev-Poincaré type inequalities