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Renormalized solutions of nonlinear parabolic equations with general measure data

Authors:

Francesco Petitta

Affiliation:

(1) Dipartimento di Matematica, Università La Sapienza, Piazzale A. Moro 2, 00185 Rome, Italy

Abstract:

Let $Omegasubseteq mathbb{R}^n$ a bounded open set, N ≥ 2, and let p > 1; we prove existence of a renormalized solution for parabolic problems whose model is

$left{ begin{array}{lll} u_t - Delta _p u = mu &{rm in},(0,T) times Omega , u(0,x) = u_0 &{rm in}, Omega , u(t,x) = 0 &{rm on}, (0,T) times partial Omega, end{array} right.$

where T > 0 is a positive constant, $$muin M(Q)$$

is a measure with bounded variation over $$Q=(0,T) times Omega, u_oin L^1(Omega)$$

, and $-Delta_{p} u=-{rm div} (|nabla u|^{p-2}nabla u )$ is the usual p-Laplacian.

Keywords:

Nonlinear parabolic equations Parabolic capacity Measure data

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