Geodesic
Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the $p(x)$-Laplacian
Claudia Lederman1 ; Noemi Wolanski1
1Universidad de Buenos Aires, Argentina
Interfaces and free boundaries, Tome 19 (2017) no. 2, pp. 201-241

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DOI

In this paper we study a one phase free boundary problem for the p(x)-Laplacian with non-zero right hand side. We prove that the free boundary of a weak solution is a C1,α surface in a neighborhood of every „flat" free boundary point. We also obtain further regularity results on the free boundary, under further regularity assumptions on the data. We apply these results to limit functions of an inhomogeneous singular perturbation problem for the p(x)-Laplacian that we studied in [25].
DOI : 10.4171/ifb/381
Classification : 35-XX
Mots-clés : Free boundary problem, variable exponent spaces, regularity of the free boundary, singular perturbation, inhomogeneous problem

Claudia Lederman  1   ; Noemi Wolanski  1

1 Universidad de Buenos Aires, Argentina 
Claudia Lederman; Noemi Wolanski. Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the $p(x)$-Laplacian. Interfaces and free boundaries, Tome 19 (2017) no. 2, pp. 201-241. doi: 10.4171/ifb/381
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     author = {Claudia Lederman and Noemi Wolanski},
     title = {Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the $p(x)${-Laplacian}},
     journal = {Interfaces and free boundaries},
     pages = {201--241},
     year = {2017},
     volume = {19},
     number = {2},
     doi = {10.4171/ifb/381},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/381/}
}
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