We consider a class of equations in divergence form with a singular/degenerate weight. Under suitable regularity assumptions for the matrix A, the forcing term f and the field F, we prove Holder continuity of solutions which are odd in y, and possibly of their derivatives. In addition, we show stability of the C0,alpha and C1,alpha a priori bounds for approximating problems. Our method is based upon blow-up and appropriate Liouville type theorems.
Liouville type theorems and regularity of solutions to degenerate or singular problems part II: odd solutions
Sire, Yannick;Vita, Stefano
2021-01-01
Abstract
We consider a class of equations in divergence form with a singular/degenerate weight. Under suitable regularity assumptions for the matrix A, the forcing term f and the field F, we prove Holder continuity of solutions which are odd in y, and possibly of their derivatives. In addition, we show stability of the C0,alpha and C1,alpha a priori bounds for approximating problems. Our method is based upon blow-up and appropriate Liouville type theorems.File in questo prodotto:
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