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Propriétés Régularisantes de Certains Semi-Groupes Non Linéaires

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Abstract

Let φ be a convex l.s.c. function fromH (Hilbert) into ] - ∞, ∞ ] andD(φ)={u ∈H; φ(u)<+∞}. It is proved that for everyu 0 ∈D(φ) the equation − (du/dt)(t ∈ ∂φ(u(t)),u(0)=u 0 has a solution satisfying ÷(du(t)/dt)÷ ≦(c 1/t)+c 2. The behavior ofu(t) in the neighborhood oft=0 andt=+∞ as well as the inhomogeneous equation (du(t)/dt)+∂φ(u(t)) ∈f(t) are then studied. Solutions of some nonlinear boundary value problems are given as applications.

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  1. Institut de Mathématique, Faculté des Sciences 11 Quai St Bernard Paris 5e, France

    H. Brézis

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  1. H. Brézis
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Brézis, H. Propriétés Régularisantes de Certains Semi-Groupes Non Linéaires. Israel J. Math. 9, 513–534 (1971). https://doi.org/10.1007/BF02771467

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  • DOI: https://doi.org/10.1007/BF02771467

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