Regularity properties for p−dead core problems and their asymptotic limit as p→∞

We study regularity issues and the limiting behavior as (Formula presented.) of non-negative solutions for elliptic equations of (Formula presented.) Laplacian type ((Formula presented.)) with a strong absorption: (Formula presented.) where (Formula presented.) is a bounded function, (Formula presen...

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Detalles Bibliográficos
Publicado: 2019
Materias:
35B65 (primary)
35J60
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00246107_v99_n1_p69_daSilva
http://hdl.handle.net/20.500.12110/paper_00246107_v99_n1_p69_daSilva
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00246107_v99_n1_p69_daSilva
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spelling paper:paper_00246107_v99_n1_p69_daSilva2023-06-08T14:52:31Z Regularity properties for p−dead core problems and their asymptotic limit as p→∞ 35B65 (primary) 35J60 We study regularity issues and the limiting behavior as (Formula presented.) of non-negative solutions for elliptic equations of (Formula presented.) Laplacian type ((Formula presented.)) with a strong absorption: (Formula presented.) where (Formula presented.) is a bounded function, (Formula presented.) is a bounded domain and (Formula presented.). When (Formula presented.) is fixed, such a model is mathematically interesting since it permits the formation of dead core zones, that is, a priori unknown regions where non-negative solutions vanish identically. First, we turn our attention to establishing sharp quantitative regularity properties for (Formula presented.) dead core solutions. Afterwards, assuming that (Formula presented.) exists, we establish existence for limit solutions as (Formula presented.), as well as we characterize the corresponding limit operator governing the limit problem. We also establish sharp (Formula presented.) regularity estimates for limit solutions along free boundary points, that is, points on (Formula presented.) where the sharp regularity exponent is given explicitly by (Formula presented.). Finally, some weak geometric and measure theoretical properties as non-degeneracy, uniform positive density, porosity and convergence of the free boundaries are proved. © 2018 London Mathematical Society 2019 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00246107_v99_n1_p69_daSilva http://hdl.handle.net/20.500.12110/paper_00246107_v99_n1_p69_daSilva
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 35B65 (primary)
35J60
spellingShingle 35B65 (primary)
35J60
Regularity properties for p−dead core problems and their asymptotic limit as p→∞
topic_facet 35B65 (primary)
35J60
description We study regularity issues and the limiting behavior as (Formula presented.) of non-negative solutions for elliptic equations of (Formula presented.) Laplacian type ((Formula presented.)) with a strong absorption: (Formula presented.) where (Formula presented.) is a bounded function, (Formula presented.) is a bounded domain and (Formula presented.). When (Formula presented.) is fixed, such a model is mathematically interesting since it permits the formation of dead core zones, that is, a priori unknown regions where non-negative solutions vanish identically. First, we turn our attention to establishing sharp quantitative regularity properties for (Formula presented.) dead core solutions. Afterwards, assuming that (Formula presented.) exists, we establish existence for limit solutions as (Formula presented.), as well as we characterize the corresponding limit operator governing the limit problem. We also establish sharp (Formula presented.) regularity estimates for limit solutions along free boundary points, that is, points on (Formula presented.) where the sharp regularity exponent is given explicitly by (Formula presented.). Finally, some weak geometric and measure theoretical properties as non-degeneracy, uniform positive density, porosity and convergence of the free boundaries are proved. © 2018 London Mathematical Society
title Regularity properties for p−dead core problems and their asymptotic limit as p→∞
title_short Regularity properties for p−dead core problems and their asymptotic limit as p→∞
title_full Regularity properties for p−dead core problems and their asymptotic limit as p→∞
title_fullStr Regularity properties for p−dead core problems and their asymptotic limit as p→∞
title_full_unstemmed Regularity properties for p−dead core problems and their asymptotic limit as p→∞
title_sort regularity properties for p−dead core problems and their asymptotic limit as p→∞
publishDate 2019
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00246107_v99_n1_p69_daSilva
http://hdl.handle.net/20.500.12110/paper_00246107_v99_n1_p69_daSilva
_version_ 1768542974275223552

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