Abstract
Let \(\Omega\subseteq \mathbb{R}^n\) a bounded open set, N ≥ 2, and let p > 1; we prove existence of a renormalized solution for parabolic problems whose model is
where T > 0 is a positive constant, \(\mu\in M(Q)\) is a measure with bounded variation over \(Q=(0,T) \times \Omega, u_o\in L^1(\Omega)\), and \(-\Delta_{p} u=-{\rm div} (|\nabla u|^{p-2}\nabla u )\) is the usual p-Laplacian.
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Petitta, F. Renormalized solutions of nonlinear parabolic equations with general measure data. Annali di Matematica 187, 563–604 (2008). https://doi.org/10.1007/s10231-007-0057-y
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DOI: https://doi.org/10.1007/s10231-007-0057-y