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.
Articolo in rivista - Articolo scientifico
Blow-up; Boundary Harnack; Degenerate and singular elliptic equations; Divergence form elliptic operator; Fermi coordinates; Fractional Laplacian; Liouville type theorems; Schauder estimates;
English
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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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/282750
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