We prove the equivalence of various capacitary strong type estimates. Some of them appear in the characterization of the measures that are admissible data for the existence of solutions to semilinear elliptic problems with power growth. Other estimates are known to characterize the measures for which the Sobolev space can be imbedded into . The motivation comes from the semilinear problems: simpler descriptions of admissible data are given. The proof surprisingly involves the theory of singular integrals with -weights.
Nous montrons l’équivalence de diverses estimations capacitaires de type fort. Certaines d’entre elles apparaissent dans la caractérisation des mesures 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 telles que l’espace de Sobolev s’injecte continûment dans . 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 .
@article{AIF_1991__41_1_117_0, author = {Adams, D. and Pierre, Michel}, title = {Capacitary strong type estimates in semilinear problems}, journal = {Annales de l'Institut Fourier}, pages = {117--135}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {41}, number = {1}, year = {1991}, doi = {10.5802/aif.1251}, mrnumber = {92m:35074}, zbl = {0741.35012}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1251/} }
TY - JOUR AU - Adams, D. AU - Pierre, Michel TI - Capacitary strong type estimates in semilinear problems JO - Annales de l'Institut Fourier PY - 1991 SP - 117 EP - 135 VL - 41 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1251/ DO - 10.5802/aif.1251 LA - en ID - AIF_1991__41_1_117_0 ER -
%0 Journal Article %A Adams, D. %A Pierre, Michel %T Capacitary strong type estimates in semilinear problems %J Annales de l'Institut Fourier %D 1991 %P 117-135 %V 41 %N 1 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.1251/ %R 10.5802/aif.1251 %G en %F AIF_1991__41_1_117_0
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://www.numdam.org/articles/10.5802/aif.1251/
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