Regularity for entropy solutions of parabolic p-Laplacian type equations.

Segura de León, Sergio, and Toledo, José. "Regularity for entropy solutions of parabolic p-Laplacian type equations.." Publicacions Matemàtiques 43.2 (1999): 665-683. <http://eudml.org/doc/41380>.

@article{SeguradeLeón1999,
abstract = {In this note we give some summability results for entropy solutions of the nonlinear parabolic equation ut - div ap (x, ∇u) = f in ] 0,T [xΩ with initial datum in L1(Ω) and assuming Dirichlet's boundary condition, where ap(.,.) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L1 (]0,T[xΩ) and Ω is a domain in RN. We find spaces of type Lr(0,T;Mq(Ω)) containing the entropy solution and its gradient. We also include some summability results when f = 0 and the p-Laplacian equation is considered.},
author = {Segura de León, Sergio, Toledo, José},
journal = {Publicacions Matemàtiques},
keywords = {Ecuaciones parabólicas; Ecuaciones en derivadas parciales no lineales; Entropía; Regularidad; Leray-Lions conditions; data; Marcinkiewicz space estimates},
language = {eng},
number = {2},
pages = {665-683},
title = {Regularity for entropy solutions of parabolic p-Laplacian type equations.},
url = {http://eudml.org/doc/41380},
volume = {43},
year = {1999},
}

TY - JOUR
AU - Segura de León, Sergio
AU - Toledo, José
TI - Regularity for entropy solutions of parabolic p-Laplacian type equations.
JO - Publicacions Matemàtiques
PY - 1999
VL - 43
IS - 2
SP - 665
EP - 683
AB - In this note we give some summability results for entropy solutions of the nonlinear parabolic equation ut - div ap (x, ∇u) = f in ] 0,T [xΩ with initial datum in L1(Ω) and assuming Dirichlet's boundary condition, where ap(.,.) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L1 (]0,T[xΩ) and Ω is a domain in RN. We find spaces of type Lr(0,T;Mq(Ω)) containing the entropy solution and its gradient. We also include some summability results when f = 0 and the p-Laplacian equation is considered.
LA - eng
KW - Ecuaciones parabólicas; Ecuaciones en derivadas parciales no lineales; Entropía; Regularidad; Leray-Lions conditions; data; Marcinkiewicz space estimates
UR - http://eudml.org/doc/41380
ER -