We construct a function which is a solution to in the sense of distributions, where A is continuous and for . We also give a function such that for every , u satisfies with A continuous but . This answers questions raised by H. Brezis (On a conjecture of J. Serrin, Rend. Lincei Mat. Appl. 19 (2008) 335–338).
Nous construisons une fonction , solution de au sens des distributions, où A est continu et pour . Nous donnons aussi une fonction telle que pour tout , u satisfait avec A continu mais . Ceci répond à des questions souleveées par H. Brezis (On a conjecture of J. Serrin, Rend. Lincei Mat. Appl. 19 (2008) 335–338).
Accepted:
Published online:
@article{CRMATH_2009__347_13-14_773_0, author = {Jin, Tianling and Maz'ya, Vladimir and Van Schaftingen, Jean}, title = {Pathological solutions to elliptic problems in divergence form with continuous coefficients}, journal = {Comptes Rendus. Math\'ematique}, pages = {773--778}, publisher = {Elsevier}, volume = {347}, number = {13-14}, year = {2009}, doi = {10.1016/j.crma.2009.05.008}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.05.008/} }
TY - JOUR AU - Jin, Tianling AU - Maz'ya, Vladimir AU - Van Schaftingen, Jean TI - Pathological solutions to elliptic problems in divergence form with continuous coefficients JO - Comptes Rendus. Mathématique PY - 2009 SP - 773 EP - 778 VL - 347 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.05.008/ DO - 10.1016/j.crma.2009.05.008 LA - en ID - CRMATH_2009__347_13-14_773_0 ER -
%0 Journal Article %A Jin, Tianling %A Maz'ya, Vladimir %A Van Schaftingen, Jean %T Pathological solutions to elliptic problems in divergence form with continuous coefficients %J Comptes Rendus. Mathématique %D 2009 %P 773-778 %V 347 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.05.008/ %R 10.1016/j.crma.2009.05.008 %G en %F CRMATH_2009__347_13-14_773_0
Jin, Tianling; Maz'ya, Vladimir; Van Schaftingen, Jean. Pathological solutions to elliptic problems in divergence form with continuous coefficients. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 773-778. doi : 10.1016/j.crma.2009.05.008. http://www.numdam.org/articles/10.1016/j.crma.2009.05.008/
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