Propagation of smallness for solutions of elliptic equations in the plane

Abstract

We explore quantitative propagation of smallness for solutions of two-dimensional elliptic equations from sets of positive $\delta$-dimensional Hausdorff content for any $\delta >0$. In particular, the gradients of solutions to divergence form equations with Hölder continuous coefficients, as well as those of nondivergence form equations with measurable coefficients, can be quantitatively estimated from the small sets.

References in corpus (1)

• Results on gradients of harmonic functions on Lipschitz surfaces

Cited by in corpus (1)

• On the dimension of observable sets for the heat equation