Abstract
The continuity of weak solutions of elliptic partial differential equations $div \mathcal{A}(x,\nabla u) = 0$ is considered under minimal structure assumptions. The main result guarantees the continuity at the point x0 for weakly monotone weak solutions if the structure of A is controlled in a sequence of annuli $B(x_0 ,R_j )\backslash \bar B(x_0 ,r_j )$ with uniformly bounded ratio Rj/rj such that limj→∞Rj=0. As a consequence, we obtain a sufficient condition for the continuity of mappings of finite distortion.
Citation
Visa Latvala. "Continuity of weak solutions of elliptic partial differential equations." Ark. Mat. 41 (1) 95 - 104, April 2003. https://doi.org/10.1007/BF02384569
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