Nous considérons des problèmes de Neumann pour des équations elliptiques non linéaires dans des domaines éventuellement non réguliers et avec des données peu régulières. Un équilibre entre l'intégrabilité de la donnée et l'(ir)régularité du domaine nous permet d'obtenir l'existence, l'unicité et la dépendance continue de solutions généralisées. L'irrégularité du domaine est décrite par des inégalités « isocapacitaires ». Nous donnons aussi des applications à certaines classes de domaines.
Non-linear elliptic Neumann problems, possibly in irregular domains and with data affected by low integrability properties, are taken into account. Existence, uniqueness and continuous dependence on the data of generalized solutions are established under a suitable balance between the integrability of the datum and the (ir)regularity of the domain. The latter is described in terms of isocapacitary inequalities. Applications to various classes of domains are also presented.
Mots-clés : Non-linear elliptic equations, Neumann problems, Generalized solutions, A priori estimates, Stability estimates, Capacity, Perimeter, Rearrangements
@article{AIHPC_2010__27_4_1017_0, author = {Alvino, Angelo and Cianchi, Andrea and Maz'ya, Vladimir G. and Mercaldo, Anna}, title = {Well-posed elliptic {Neumann} problems involving irregular data and domains}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1017--1054}, publisher = {Elsevier}, volume = {27}, number = {4}, year = {2010}, doi = {10.1016/j.anihpc.2010.01.010}, mrnumber = {2659156}, zbl = {1200.35105}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2010.01.010/} }
TY - JOUR AU - Alvino, Angelo AU - Cianchi, Andrea AU - Maz'ya, Vladimir G. AU - Mercaldo, Anna TI - Well-posed elliptic Neumann problems involving irregular data and domains JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 1017 EP - 1054 VL - 27 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2010.01.010/ DO - 10.1016/j.anihpc.2010.01.010 LA - en ID - AIHPC_2010__27_4_1017_0 ER -
%0 Journal Article %A Alvino, Angelo %A Cianchi, Andrea %A Maz'ya, Vladimir G. %A Mercaldo, Anna %T Well-posed elliptic Neumann problems involving irregular data and domains %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 1017-1054 %V 27 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2010.01.010/ %R 10.1016/j.anihpc.2010.01.010 %G en %F AIHPC_2010__27_4_1017_0
Alvino, Angelo; Cianchi, Andrea; Maz'ya, Vladimir G.; Mercaldo, Anna. Well-posed elliptic Neumann problems involving irregular data and domains. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 4, pp. 1017-1054. doi : 10.1016/j.anihpc.2010.01.010. http://www.numdam.org/articles/10.1016/j.anihpc.2010.01.010/
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