On the notion of renormalized solution to nonlinear parabolic equations with general measure data

Francesco Petitta; Alessio Porretta

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arXiv · 1506.03671

On the notion of renormalized solution to nonlinear parabolic equations with general measure data

Francesco Petitta·Alessio Porretta

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Abstract

Here we introduce a new notion of renormalized solution to nonlinear parabolic problems with general measure data whose model is $$ \begin{cases} u_t-\Delta_{p} u =\mu & \text{in}\ (0,T)\times\Omega, u=u_0 & \text{on}\ \{0\} \times \Omega, u=0 &\text{on}\ (0,T)\times\partial\Omega, \end{cases} $$ for any, possibly singular, nonnegative bounded measure $\mu$. We prove existence of such a solutions and we discuss their main properties.

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Francesco Petitta, Alessio Porretta. 2015-06-11. On the notion of renormalized solution to nonlinear parabolic equations with general measure data. https://arxiv.org/abs/1506.03671

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