Nous donnons une demonstration très simple de l'unicité des solutions entropiques de problèmes de Dirichlet dans L1.
We give here a short proof of the uniqueness of entropy solutions for nonlinear monotone elliptic problems with L1-data.
Accepté le :
Publié le :
@article{CRMATH_2003__337_5_313_0, author = {Porzio, Maria Michaela}, title = {A uniqueness result for monotone elliptic problems}, journal = {Comptes Rendus. Math\'ematique}, pages = {313--316}, publisher = {Elsevier}, volume = {337}, number = {5}, year = {2003}, doi = {10.1016/S1631-073X(03)00347-9}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/S1631-073X(03)00347-9/} }
TY - JOUR AU - Porzio, Maria Michaela TI - A uniqueness result for monotone elliptic problems JO - Comptes Rendus. Mathématique PY - 2003 SP - 313 EP - 316 VL - 337 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(03)00347-9/ DO - 10.1016/S1631-073X(03)00347-9 LA - en ID - CRMATH_2003__337_5_313_0 ER -
%0 Journal Article %A Porzio, Maria Michaela %T A uniqueness result for monotone elliptic problems %J Comptes Rendus. Mathématique %D 2003 %P 313-316 %V 337 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(03)00347-9/ %R 10.1016/S1631-073X(03)00347-9 %G en %F CRMATH_2003__337_5_313_0
Porzio, Maria Michaela. A uniqueness result for monotone elliptic problems. Comptes Rendus. Mathématique, Tome 337 (2003) no. 5, pp. 313-316. doi : 10.1016/S1631-073X(03)00347-9. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00347-9/
[1] An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., Volume 22 (1995), pp. 241-273
[2] Some nonlinear Dirichlet problems in L1 involving lower order terms in divergence form, Progress in Elliptic and Parabolic Partial Differential Equations (Capri, 1994), Pitman Res. Notes Math. Ser., 350, Longman, Harlow, 1996, pp. 43-57
[3] Semi-linear second-order elliptic equations in L1, J. Math. Soc. Japan, Volume 25 (1973) no. 4, pp. 565-590
[4] Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures, Rend. Mat., Volume 15 (1995), pp. 321-337
[5] Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., Volume 18 (1964), pp. 385-387
[6] Le probléme de Dirichlet pour les équations elliptiques du second ordre á coefficients discontinus, Ann. Inst. Fourier (Grenoble), Volume 15 (1965), pp. 189-258
Cité par Sources :