A proof of the C-p %26apos;-regularity conjecture in the plane

作者：Araujo Damido J; Teixeira Eduardo V; Urbano Jose Miguel

来源：Advances in Mathematics, 2017, 316: 541-553.

DOI：10.1016/j.aim.2017.06.027

• Nonlinear pdes
• Regularity theory
• Sharp estimates

We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class C-p' = C-1'1/p-1 this regularity is optimal. Published by Elsevier Inc.

• 出版日期2017-8-20