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

Sergio Segura de León; José Toledo

Publicacions Matemàtiques (1999)

- Volume: 43, Issue: 2, page 665-683
- ISSN: 0214-1493

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topSegura 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 -