We give necessary and sufficient conditions for the existence of a BMO solution to the quasilinear equation in , , where is a locally finite Radon measure, and is the -Laplacian ().
We also characterize BMO solutions to equations in , , with , where both and are locally finite Radon measures. Our main results hold for a class of more general quasilinear operators in place of .
Nous donnons les conditions nécessaires et suffisantes pour l’existence d’une solution BMO de l’équation quasi-linéaire dans , , où est une mesure de Radon localement finie, et est le -Laplacien ().
Nous caractérisons également les solutions BMO de l’équation dans , , avec , où et sont des mesures de Radon localement finies. Nos principaux résultats sont valables pour la classe plus générale des opérateurs quasi-linéaires plus généraux à la place de .
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Keywords: BMO spaces, Wolff potentials, -Laplacian
@unpublished{AIF_0__0_0_A79_0, author = {Phuc, Nguyen Cong and Verbitsky, Igor E.}, title = {BMO solutions to quasilinear equations of $p${-Laplace} type}, journal = {Annales de l'Institut Fourier}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, year = {2022}, doi = {10.5802/aif.3485}, language = {en}, note = {Online first}, }
Phuc, Nguyen Cong; Verbitsky, Igor E. BMO solutions to quasilinear equations of $p$-Laplace type. Annales de l'Institut Fourier, Online first, 29 p.
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