Parabolic Capacity and Soft Measures for Nonlinear Equations |
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| Authors: | Droniou Jérôme Porretta Alessio Prignet Alain |
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| Institution: | (1) CMI, Université de Provence, 39 Rue F. Joliot Curie, 13453 Marseille Cedex 13, France;(2) Dipartimento di Matematica, Università di Roma II, Via della Ricerca Scientifica, 00133 Roma, Italy;(3) Mathématiques, Université d'Orléans, Rue de Chartres, 45067 Orléans Cedex 2, France |
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| Abstract: | We first introduce, using a functional approach, the notion of capacity related to the parabolic p-Laplace operator. Then we prove a decomposition theorem for measures (in space and time) that do not charge the sets of null capacity. We apply this result to prove existence and uniqueness of renormalized solutions for nonlinear parabolic initial boundary-value problems with such measures as right-hand side. |
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| Keywords: | parabolic equations measure capacity |
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