Artículo
Nontrivial compact blow-up sets of lower dimension in a half-space
Autor/es | Pérez Llanos, Mayte
Rossi Pérez, Julio Daniel |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones diferenciales y Análisis numérico |
Fecha de publicación | 2007-09-01 |
Fecha de depósito | 2022-01-10 |
Publicado en |
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Resumen | In this paper we provide examples of blowing-up solutions to parabolic problems in a half space, RN+×RM={xN>0}×RMR+N×RM={xN>0}×RM, with nontrivial blow-up sets of dimension strictly smaller than the space dimension. To ... In this paper we provide examples of blowing-up solutions to parabolic problems in a half space, RN+×RM={xN>0}×RMR+N×RM={xN>0}×RM, with nontrivial blow-up sets of dimension strictly smaller than the space dimension. To this end we prove existence of a nontrivial compactly supported solution to ∇(|∇φ|p−2∇φ)=φ∇(|∇φ|p−2∇φ)=φ in the half space RN+={xN>0}R+N={xN>0} with the nonlinear boundary condition −|∇φ|p−2∂φ∂xN=φp−1−|∇φ|p−2∂φ∂xN=φp−1 on ∂RN+={xN=0}∂R+N={xN=0}. |
Cita | Pérez Llanos, M. y Rossi Pérez, J.D. (2007). Nontrivial compact blow-up sets of lower dimension in a half-space. Differential Integral Equations, 20 (11), 1211-1228. |
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