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Abstract:

In this manuscript we study geometric regularity estimates for quasi-linear elliptic equations of p-Laplace type (1 < p< ∞) with strong absorption condition: (Formula presented.). R+× RN→ RNis a vector field with an appropriate p-structure, λ0is a non-negative and bounded function and 0 ≤ q< p- 1. Such a model permits existence of solutions with dead core zones, i.e, a priori unknown regions where non-negative solutions vanish identically. We establish sharp and improved Cγregularity estimates along free boundary points, namely F0(u, Ω) = ∂{ u> 0 } ∩ Ω , where the regularity exponent is given explicitly by γ=pp-1-q≫1. Some weak geometric and measure theoretical properties as non-degeneracy, uniform positive density and porosity of free boundary are proved. As an application, a Liouville-type result for entire solutions is established provided that their growth at infinity can be controlled in an appropriate manner. Finally, we obtain finiteness of (N- 1) -Hausdorff measure of free boundary for a particular class of dead core problems. The approach employed in this article is novel even to dead core problems governed by the p-Laplace operator - Δ pu+ λ0uqχ{ u > 0 }= 0 for any λ0> 0. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

Registro:

Documento: Artículo
Título:Sharp regularity estimates for quasi-linear elliptic dead core problems and applications
Autor:da Silva, J.V.; 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; 35J60
Año:2018
Volumen:57
Número:3
DOI: http://dx.doi.org/10.1007/s00526-018-1344-8
Título revista:Calculus of Variations and Partial Differential Equations
Título revista abreviado:Calc. Var. Partial Differ. Equ.
ISSN:09442669
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09442669_v57_n3_p_daSilva

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Citas:

---------- APA ----------
da Silva, J.V. & Salort, A.M. (2018) . Sharp regularity estimates for quasi-linear elliptic dead core problems and applications. Calculus of Variations and Partial Differential Equations, 57(3).
http://dx.doi.org/10.1007/s00526-018-1344-8
---------- CHICAGO ----------
da Silva, J.V., Salort, A.M. "Sharp regularity estimates for quasi-linear elliptic dead core problems and applications" . Calculus of Variations and Partial Differential Equations 57, no. 3 (2018).
http://dx.doi.org/10.1007/s00526-018-1344-8
---------- MLA ----------
da Silva, J.V., Salort, A.M. "Sharp regularity estimates for quasi-linear elliptic dead core problems and applications" . Calculus of Variations and Partial Differential Equations, vol. 57, no. 3, 2018.
http://dx.doi.org/10.1007/s00526-018-1344-8
---------- VANCOUVER ----------
da Silva, J.V., Salort, A.M. Sharp regularity estimates for quasi-linear elliptic dead core problems and applications. Calc. Var. Partial Differ. Equ. 2018;57(3).
http://dx.doi.org/10.1007/s00526-018-1344-8