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Abstract:

In this manuscript, we study geometric regularity estimates for degenerate parabolic equations of p-Laplacian type (2≤p<∞) under a strong absorption condition: Δpu−[Formula presented]=λ0u+ qinΩT:=Ω×(0,T), where 0≤q<1. This model is interesting because it yields the formation of dead-core sets, i.e., regions where non-negative solutions vanish identically. We shall prove sharp and improved parabolic Cα regularity estimates along the set F0(u,ΩT)=∂{u>0}∩ΩT (the free boundary), where α=[Formula presented]≥1+[Formula presented]. Some weak geometric and measure theoretical properties as non-degeneracy, positive density, porosity and finite speed of propagation are proved. As an application, we prove a Liouville-type result for entire solutions. A specific analysis for Blow-up type solutions will be done as well. The results are new even for dead-core problems driven by the heat operator. © 2018 Elsevier Inc.

Registro:

Documento: Artículo
Título:Regularity for degenerate evolution equations with strong absorption
Autor:da Silva, J.V.; Ochoa, P.; Silva, A.
Filiación:Universidad de Buenos Aires, Departamento de Matemática, FCEyN, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
Universidad Nacional de Cuyo, CONICET, Mendoza, 5500, Argentina
Instituto de Matemática Aplicada San Luis-IMASL, Universidad Nacional de San Luis, CONICET, Ejercito de los Andes 950, San Luis, D5700HHW, Argentina
Palabras clave:Dead-core problems; Liouville type results; p-Laplacian type operators; Sharp and improved intrinsic regularity
Año:2018
Volumen:264
Número:12
Página de inicio:7270
Página de fin:7293
DOI: http://dx.doi.org/10.1016/j.jde.2018.02.013
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.
ISSN:00220396
CODEN:JDEQA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v264_n12_p7270_daSilva

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Citas:

---------- APA ----------
da Silva, J.V., Ochoa, P. & Silva, A. (2018) . Regularity for degenerate evolution equations with strong absorption. Journal of Differential Equations, 264(12), 7270-7293.
http://dx.doi.org/10.1016/j.jde.2018.02.013
---------- CHICAGO ----------
da Silva, J.V., Ochoa, P., Silva, A. "Regularity for degenerate evolution equations with strong absorption" . Journal of Differential Equations 264, no. 12 (2018) : 7270-7293.
http://dx.doi.org/10.1016/j.jde.2018.02.013
---------- MLA ----------
da Silva, J.V., Ochoa, P., Silva, A. "Regularity for degenerate evolution equations with strong absorption" . Journal of Differential Equations, vol. 264, no. 12, 2018, pp. 7270-7293.
http://dx.doi.org/10.1016/j.jde.2018.02.013
---------- VANCOUVER ----------
da Silva, J.V., Ochoa, P., Silva, A. Regularity for degenerate evolution equations with strong absorption. J. Differ. Equ. 2018;264(12):7270-7293.
http://dx.doi.org/10.1016/j.jde.2018.02.013