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Abstract:

In this manuscript we deal with regularity issues and the asymptotic behaviour (as p→ ∞) of solutions for elliptic free boundary problems of p- Laplacian type (2 ≤ p< ∞): -Δpu(x)+λ0(x)χ{u>0}(x)=0inΩ⊂RN,with a prescribed Dirichlet boundary data, where λ> 0 is a bounded function and Ω is a regular domain. First, we prove the convergence as p→ ∞ of any family of solutions (up)p≥2, as well as we obtain the corresponding limit operator (in non-divergence form) ruling the limit equation, {max{-Δ∞u∞,-|∇u∞|+χ{u∞>0}}=0inΩ∩{u∞≥0}u∞=Fon∂Ω.Next, we obtain uniqueness for solutions to this limit problem. Finally, we show that any solution to the limit operator is a limit of value functions for a specific Tug-of-War game. © 2019, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.

Registro:

Documento: Artículo
Título:A limiting free boundary problem with gradient constraint and Tug-of-War games
Autor:Blanc, P.; da Silva, J.V.; Rossi, J.D.
Filiación:FCEyN, Department of Mathematics, Universidad de Buenos Aires, Ciudad Universitaria-Pabellón, Buenos Aires, C1428EGA, Argentina
Palabras clave:Existence/uniqueness of solutions; Free boundary problems; Lipschitz regularity estimates; Tug-of-War games; ∞-Laplace operator
Año:2019
DOI: http://dx.doi.org/10.1007/s10231-019-00825-0
Título revista:Annali di Matematica Pura ed Applicata
Título revista abreviado:Ann. Mat. Pura Appl.
ISSN:03733114
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_03733114_v_n_p_Blanc

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Citas:

---------- APA ----------
Blanc, P., da Silva, J.V. & Rossi, J.D. (2019) . A limiting free boundary problem with gradient constraint and Tug-of-War games. Annali di Matematica Pura ed Applicata.
http://dx.doi.org/10.1007/s10231-019-00825-0
---------- CHICAGO ----------
Blanc, P., da Silva, J.V., Rossi, J.D. "A limiting free boundary problem with gradient constraint and Tug-of-War games" . Annali di Matematica Pura ed Applicata (2019).
http://dx.doi.org/10.1007/s10231-019-00825-0
---------- MLA ----------
Blanc, P., da Silva, J.V., Rossi, J.D. "A limiting free boundary problem with gradient constraint and Tug-of-War games" . Annali di Matematica Pura ed Applicata, 2019.
http://dx.doi.org/10.1007/s10231-019-00825-0
---------- VANCOUVER ----------
Blanc, P., da Silva, J.V., Rossi, J.D. A limiting free boundary problem with gradient constraint and Tug-of-War games. Ann. Mat. Pura Appl. 2019.
http://dx.doi.org/10.1007/s10231-019-00825-0