Displaying similar documents to “Local and global integrability of gradients in obstacle problems.”

Continuity of solutions of linear, degenerate elliptic equations

Jani Onninen, Xiao Zhong (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

We consider the simplest form of a second order, linear, degenerate, elliptic equation with divergence structure in the plane. Under an integrability condition on the degenerate function, we prove that the solutions are continuous.

Estimates on elliptic equations that hold only where the gradient is large

Cyril Imbert, Luis Silvestre (2016)

Journal of the European Mathematical Society

Similarity:

We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the Hölder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.