Fonctions à hessien borné
Annales de l'Institut Fourier, Tome 34 (1984) no. 2, pp. 155-190.

Cet article établit quelques propriétés des distributions sur un ouvert Ω de RN dont le hessien est une mesure bornée. Après quelques propriétés topologiques – Compacité faible des bornées de HB(Ω) lorsque Ω est borné, densité des fonctions régulières pour une topologie assez finie – on s’intéresse au comportement sur le bord de Ω lorsque ∂Ω est assez régulier; pour ce faire, on est amené à étudier celui des fonctions de W2,1. On montre enfin dans une 3ème partie des théorèmes d’injection de Sobolev et notamment la continuité de telles fonctions.

This paper is concerned with some properties of distributions defined on an open set of RN the hessian of which is a bounded measure. We first state topological properties, as the weak compacity of bounded sets of HB(Ω) when Ω is bounded, the density of smooth functions for a topology sufficiently sharp. Then we address the questions of the behavior of such distribution on the boundary of Ω. This leads us to study the same question for functions of W2,1(Ω). Finally, we prove Sobolev imbedding Theorems appropriate in this context and specifically imbedding into some set of continuous functions.

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Demengel, Françoise. Fonctions à hessien borné. Annales de l'Institut Fourier, Tome 34 (1984) no. 2, pp. 155-190. doi : 10.5802/aif.969. https://www.numdam.org/articles/10.5802/aif.969/

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