Geodesic
Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case
Electronic journal of differential equations, Tome 2004 (2004)
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},
     year = {2004},
     volume = {2004},
     zbl = {1217.35217},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a26/}
}
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AU  - Weiss,  Georg S.
TI  - Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case
JO  - Electronic journal of differential equations
PY  - 2004
VL  - 2004
UR  - http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a26/
LA  - en
ID  - EJDE_2004__2004__a26
ER  - 
%0 Journal Article
%A Weiss,  Georg S.
%T Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case
%J Electronic journal of differential equations
%D 2004
%V 2004
%U http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a26/
%G en
%F EJDE_2004__2004__a26
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/