Geodesic
Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We derive a monotonicity formula at boundary points for a class of nonlinear elliptic partial differential equations, including the obstacle problem case, quenching, a free boundary problem with Bernoulli-type free boundary condition as well as the blow-up case. As application model we prove - for Dirichlet boundary data satisfying certain assumptions - the global existence of a classical solution of the free boundary problem with Bernoulli-type free boundary condition in two and three dimensions.
Classification : 35R35, 35J67, 35J60
Keywords: free boundary, boundary regularity, non-tangential touch, monotonicity formula, global regularity, Bernoulli-type free boundary condition 
@article{EJDE_2004__2004__a26,
     author = {Weiss, Georg S.},
     title = {Boundary monotonicity formulae and applications to free boundary problems {I:} {The} elliptic case},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a26/}
}
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Weiss, Georg S. Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a26/