We consider a class of equations in divergence form with a singular/degenerate weight (equation presented) Under suitable regularity assumptions for the matrix A, the forcing term f and the field F, we prove Hölder continuity of solutions which are odd in y 2 R, and possibly of their derivatives. In addition, we show stability of the C0;α and C1;α a priori bounds for approximating problems in the form (equation presented) as ϵ → 0. Our method is based upon blow-up and appropriate Liouville type theorems.
Sire, Y., Terracini, S., Vita, S. (2021). Liouville type theorems and regularity of solutions to degenerate or singular problems part II: odd solutions. MATHEMATICS IN ENGINEERING, 3(1), 1-50 [10.3934/mine.2021005].
Liouville type theorems and regularity of solutions to degenerate or singular problems part II: odd solutions
Terracini, S
;Vita, S
2021
Abstract
We consider a class of equations in divergence form with a singular/degenerate weight (equation presented) Under suitable regularity assumptions for the matrix A, the forcing term f and the field F, we prove Hölder continuity of solutions which are odd in y 2 R, and possibly of their derivatives. In addition, we show stability of the C0;α and C1;α a priori bounds for approximating problems in the form (equation presented) as ϵ → 0. Our method is based upon blow-up and appropriate Liouville type theorems.
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