Capacitary strong type estimates in semilinear problems
Annales de l'Institut Fourier, Volume 41 (1991) no. 1, pp. 117-135.

We prove the equivalence of various capacitary strong type estimates. Some of them appear in the characterization of the measures μ that are admissible data for the existence of solutions to semilinear elliptic problems with power growth. Other estimates are known to characterize the measures μ for which the Sobolev space W 2,p can be imbedded into L p (μ). The motivation comes from the semilinear problems: simpler descriptions of admissible data are given. The proof surprisingly involves the theory of singular integrals with A p -weights.

Nous montrons l’équivalence de diverses estimations capacitaires de type fort. Certaines d’entre elles apparaissent dans la caractérisation des mesures μ qui sont admissibles pour l’existence de solutions de problèmes elliptiques semi-linéaires avec croissance polynomiale. D’autres sont bien connues comme caractérisant les mesures μ telles que l’espace de Sobolev W 2,p s’injecte continûment dans L p (μ). La motivation vient essentiellement des problèmes semilinéaires : des descriptions très simples des données admissibles peuvent être ainsi données. La démonstration utilise de façon assez surprenenante la théorie des intégrales singulières avec poids de type A p .

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Adams, D.; Pierre, Michel. Capacitary strong type estimates in semilinear problems. Annales de l'Institut Fourier, Volume 41 (1991) no. 1, pp. 117-135. doi : 10.5802/aif.1251. http://archive.numdam.org/articles/10.5802/aif.1251/

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