Liouville type theorems and regularity of solutions to degenerate or singular problems part I: even solutions

By Yannick Sire, S. Terracini, Stefano Finzi Vita. 2019

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Abstract We consider a class of equations in divergence form with a singular/degenerate weight Under suitable regularity assumptions for the matrix A and f (resp. F) we prove Hölder continuity of solutions which are even in and possibly of their derivatives up to order two or more (Schauder estimates). In addition, we show stability of the and a priori bounds for approximating problems in the form as Finally, we derive and bounds for inhomogenous Neumann boundary problems as well. Our method is based upon blow-up and appropriate Liouville type theorems.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/6423965e828d98628f5d2c6fcff1c64379e3de34