Geodesic
The maximum principle for equations with composite coefficients
Electronic journal of differential equations, Tome 2000 (2000)
It is well-known that the maximum of the solution of a linear elliptic equation can be estimated in terms of the boundary data provided the coefficient of the gradient term is either integrable to an appropriate power or blows up like a small negative power of distance to the boundary. Apushkinskaya and Nazarov showed that a similar estimate holds if this term is a sum of such functions provided the boundary of the domain is sufficiently smooth and a Dirichlet condition is prescribed. We relax the smoothness of the boundary and also consider non-Dirichlet boundary conditions using a variant of the method of Apushkinskaya and Nazarov. In addition, we prove a Holder estimate for solutions of oblique derivative problems for nonlinear equations satisfying similar conditions.
Classification : 35J25, 35B50, 35J65, 35B45, 35K20
Keywords: elliptic differential equations, oblique boundary conditions, maximum principles, holder estimates, Harnack inequality, parabolic differential equations 
@article{EJDE_2000__2000__a176,
     author = {Lieberman,  Gary M.},
     title = {The maximum principle for equations with composite coefficients},
     journal = {Electronic journal of differential equations},
     year = {2000},
     volume = {2000},
     zbl = {0952.35025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a176/}
}
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JO  - Electronic journal of differential equations
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VL  - 2000
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%0 Journal Article
%A Lieberman,  Gary M.
%T The maximum principle for equations with composite coefficients
%J Electronic journal of differential equations
%D 2000
%V 2000
%U http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a176/
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%F EJDE_2000__2000__a176
Lieberman,  Gary M. The maximum principle for equations with composite coefficients. Electronic journal of differential equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a176/