Regularity for entropy solutions of parabolic p-Laplacian type equations.
Segura de León, Sergio ; Toledo, José
Publicacions Matemàtiques, Tome 43 (1999), p. 665-683 / Harvested from Biblioteca Digital de Matemáticas
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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.

Publié le : 1999-01-01
DMLE-ID : 3905 
@article{urn:eudml:doc:41380,
     title = {Regularity for entropy solutions of parabolic p-Laplacian type equations.},
     journal = {Publicacions Matem\`atiques},
     volume = {43},
     year = {1999},
     pages = {665-683},
     mrnumber = {MR1744624},
     zbl = {0962.35108},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41380}
}

Segura de León, Sergio; Toledo, José. Regularity for entropy solutions of parabolic p-Laplacian type equations.. Publicacions Matemàtiques, Tome 43 (1999) pp. 665-683. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41380/