We announce some recent results on boundedness and Hölder continuity up to the boundary for the weak solutions to coercive quasilinear equations with data belonging to Morrey spaces.
Nous annonçons quelques résultats récents sur la régularité höldérienne globale pour les solutions faibles d'équations coercitives quasi linéaires avec des données appartenant à des espaces de Morrey.
Accepted:
Published online:
Sun-Sig Byun 1; Dian K. Palagachev 2; Pilsoo Shin 1
@article{CRMATH_2015__353_8_717_0, author = {Sun-Sig Byun and Dian K. Palagachev and Pilsoo Shin}, title = {Global continuity of solutions to quasilinear equations with {Morrey} data}, journal = {Comptes Rendus. Math\'ematique}, pages = {717--721}, publisher = {Elsevier}, volume = {353}, number = {8}, year = {2015}, doi = {10.1016/j.crma.2015.06.003}, language = {en}, }
TY - JOUR AU - Sun-Sig Byun AU - Dian K. Palagachev AU - Pilsoo Shin TI - Global continuity of solutions to quasilinear equations with Morrey data JO - Comptes Rendus. Mathématique PY - 2015 SP - 717 EP - 721 VL - 353 IS - 8 PB - Elsevier DO - 10.1016/j.crma.2015.06.003 LA - en ID - CRMATH_2015__353_8_717_0 ER -
Sun-Sig Byun; Dian K. Palagachev; Pilsoo Shin. Global continuity of solutions to quasilinear equations with Morrey data. Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 717-721. doi : 10.1016/j.crma.2015.06.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.06.003/
[1] Traces of potentials arising from translation invariant operators, Ann. Sc. Norm. Super. Pisa (3), Volume 25 (1971), pp. 203-217
[2] Boundedness of the weak solutions to quasilinear elliptic equations with Morrey data, Indiana Univ. Math. J., Volume 62 (2013), pp. 1565-1585
[3] Global Hölder continuity of solutions to quasilinear equations with Morrey data, 2015 | arXiv
[4] Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino, Cl. Sci. Fis. Mat. Nat. (3) (1957), pp. 25-43
[5] A regularity condition at the boundary for solutions of quasilinear elliptic equations, Arch. Ration. Mech. Anal., Volume 67 (1977), pp. 25-39
[6] On some non-linear elliptic differential-functional equations, Acta Math., Volume 115 (1966), pp. 271-310
[7] Linear and Quasilinear Equations of Elliptic Type, Nauka, Moscow, 1973 (in Russian)
[8] Uniformly fat sets, Trans. Amer. Math. Soc., Volume 308 (1988), pp. 177-196
[9] On the smoothness of superharmonics which solve a minimum problem, J. Anal. Math., Volume 23 (1970), pp. 227-236
[10] Sharp forms of estimates for subsolutions and supersolutions of quasilinear elliptic equations involving measures, Commun. Partial Differ. Equ., Volume 18 (1993), pp. 1191-1212
[11] Second order elliptic equations in several variables and Hölder continuity, Math. Z., Volume 72 (1959–1960), pp. 146-164
[12] Inclusioni tra spazi di Morrey, Boll. Unione Mat. Ital. (4), Volume 2 (1969), pp. 95-99
[13] Local behavior of solutions of quasi-linear equations, Acta Math., Volume 111 (1964), pp. 247-302
[14] Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble), Volume 15 (1965), pp. 189-258
[15] On Harnack type inequalities and their application to quasilinear elliptic equations, Commun. Pure Appl. Math., Volume 20 (1967), pp. 721-747
Cited by Sources:
Comments - Policy