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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


Documento: Artículo
Título:Regularity properties for p−dead core problems and their asymptotic limit as p→∞
Autor:da Silva, J.V.; Rossi, J.D.; Salort, A.M.
Filiación:Departamento de Matemática, FCEyN - Universidad de Buenos Aires and IMAS - CONICET, Ciudad Universitaria, Pabellón I (1428) Av. Cantilo s/n, Buenos Aires, Argentina
Palabras clave:35B65 (primary); 35J60
Página de inicio:69
Página de fin:96
Título revista:Journal of the London Mathematical Society
Título revista abreviado:J. Lond. Math. Soc.


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---------- APA ----------
da Silva, J.V., Rossi, J.D. & Salort, A.M. (2019) . Regularity properties for p−dead core problems and their asymptotic limit as p→∞. Journal of the London Mathematical Society, 99(1), 69-96.
---------- CHICAGO ----------
da Silva, J.V., Rossi, J.D., Salort, A.M. "Regularity properties for p−dead core problems and their asymptotic limit as p→∞" . Journal of the London Mathematical Society 99, no. 1 (2019) : 69-96.
---------- MLA ----------
da Silva, J.V., Rossi, J.D., Salort, A.M. "Regularity properties for p−dead core problems and their asymptotic limit as p→∞" . Journal of the London Mathematical Society, vol. 99, no. 1, 2019, pp. 69-96.
---------- VANCOUVER ----------
da Silva, J.V., Rossi, J.D., Salort, A.M. Regularity properties for p−dead core problems and their asymptotic limit as p→∞. J. Lond. Math. Soc. 2019;99(1):69-96.