Soit , avec et , un opérateur non local d'ordre zéro qui approche le laplacien fractionnaire lorsque ϵ tend vers 0. Nous étudions dans cette Note les symétries des solutions de l'équation (E) : dans la boule unité ouverte avec la condition sur le complémentaire de la boule unité fermée. Nous observons que les propriétés de symétrie dépendent de la constante de Lipschitz de f. Lorsque cette constante de Lipschitz est majorée par , toute solution de (E) satisfaisant dans et sur le bord est radialement symétrique.
In this note, we study symmetry results of solutions to equation (E) in with the condition in , where , with and , is a zero-order nonlocal operator, which approaches the fractional Laplacian when . The function f is locally Lipschitz continuous. We analyzed that the symmetry properties of solutions depend on the Lipschitz constant of f. When the Lipschitz constant is controlled by , any solution of (E) satisfying in and on is radially symmetric.
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@article{CRMATH_2016__354_3_277_0, author = {dos Prazeres, Disson and Wang, Ying}, title = {Symmetry results for solutions of equations involving zero-order operators}, journal = {Comptes Rendus. Math\'ematique}, pages = {277--281}, publisher = {Elsevier}, volume = {354}, number = {3}, year = {2016}, doi = {10.1016/j.crma.2015.12.013}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2015.12.013/} }
TY - JOUR AU - dos Prazeres, Disson AU - Wang, Ying TI - Symmetry results for solutions of equations involving zero-order operators JO - Comptes Rendus. Mathématique PY - 2016 SP - 277 EP - 281 VL - 354 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2015.12.013/ DO - 10.1016/j.crma.2015.12.013 LA - en ID - CRMATH_2016__354_3_277_0 ER -
%0 Journal Article %A dos Prazeres, Disson %A Wang, Ying %T Symmetry results for solutions of equations involving zero-order operators %J Comptes Rendus. Mathématique %D 2016 %P 277-281 %V 354 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2015.12.013/ %R 10.1016/j.crma.2015.12.013 %G en %F CRMATH_2016__354_3_277_0
dos Prazeres, Disson; Wang, Ying. Symmetry results for solutions of equations involving zero-order operators. Comptes Rendus. Mathématique, Tome 354 (2016) no. 3, pp. 277-281. doi : 10.1016/j.crma.2015.12.013. http://archive.numdam.org/articles/10.1016/j.crma.2015.12.013/
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