Let Omega subset of R-N a bounded open set, N >= 2, and let p > 1; we prove existence of a renormalized solution for parabolic problems whose model is {u(t) - Delta(p)u = mu in (0, T) x Omega, u(0, x) = u(0) in Omega, u(t, x) = 0 on (0, T) x partial derivative Omega, where T > 0 is a positive constant, mu epsilon M(Q) is a measure with bounded variation over Q = ( 0, T) x Omega, u(0) epsilon L-1(Omega), and -Delta(p)u = -div(vertical bar del u vertical bar(p-2)del u) is the usual p-Laplacian.

Renormalized solutions of nonlinear parabolic equations with general measure data / Petitta, Francesco. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 187:4(2008), pp. 563-604. [10.1007/s10231-007-0057-y]

Renormalized solutions of nonlinear parabolic equations with general measure data

PETITTA, FRANCESCO
2008

Abstract

Let Omega subset of R-N a bounded open set, N >= 2, and let p > 1; we prove existence of a renormalized solution for parabolic problems whose model is {u(t) - Delta(p)u = mu in (0, T) x Omega, u(0, x) = u(0) in Omega, u(t, x) = 0 on (0, T) x partial derivative Omega, where T > 0 is a positive constant, mu epsilon M(Q) is a measure with bounded variation over Q = ( 0, T) x Omega, u(0) epsilon L-1(Omega), and -Delta(p)u = -div(vertical bar del u vertical bar(p-2)del u) is the usual p-Laplacian.
2008
measure data; nonlinear parabolic equations; parabolic capacity
01 Pubblicazione su rivista::01a Articolo in rivista
Renormalized solutions of nonlinear parabolic equations with general measure data / Petitta, Francesco. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 187:4(2008), pp. 563-604. [10.1007/s10231-007-0057-y]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/342721
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