In this paper we study the behaviour of the free boundary close to its contact points with the fixed boundary in the obstacle type problem
Let be the free boundary and assume that the origin is a contact point, i.e. . We prove that the free boundary touches the fixed boundary uniformly tangentially at the origin, near to the origin it is the graph of a function and there is a uniform modulus of continuity for the derivatives of this function.
Mots clés : Free boundary, Obstacle problem, Singular coefficient, Regularity of free boundaries
@article{AIHPC_2017__34_2_293_0, author = {Shahgholian, Henrik and Yeressian, Karen}, title = {The obstacle problem with singular coefficients near {Dirichlet} data}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {293--334}, publisher = {Elsevier}, volume = {34}, number = {2}, year = {2017}, doi = {10.1016/j.anihpc.2015.12.003}, mrnumber = {3610934}, zbl = {1515.35369}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2015.12.003/} }
TY - JOUR AU - Shahgholian, Henrik AU - Yeressian, Karen TI - The obstacle problem with singular coefficients near Dirichlet data JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 293 EP - 334 VL - 34 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2015.12.003/ DO - 10.1016/j.anihpc.2015.12.003 LA - en ID - AIHPC_2017__34_2_293_0 ER -
%0 Journal Article %A Shahgholian, Henrik %A Yeressian, Karen %T The obstacle problem with singular coefficients near Dirichlet data %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 293-334 %V 34 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2015.12.003/ %R 10.1016/j.anihpc.2015.12.003 %G en %F AIHPC_2017__34_2_293_0
Shahgholian, Henrik; Yeressian, Karen. The obstacle problem with singular coefficients near Dirichlet data. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 2, pp. 293-334. doi : 10.1016/j.anihpc.2015.12.003. http://www.numdam.org/articles/10.1016/j.anihpc.2015.12.003/
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