Geodesic
A class of nonlinear elliptic variational inequalities: Qualitative properties and existence of solutions
Electronic journal of differential equations, Tome 2002 (2002)
We study a class of nonlinear elliptic variational inequalities in divergence form. In the recent paper [6], we obtained results on the local control of essential infimum and supremum of solutions of quasilinear elliptic equations, and here we extend this point of view to the case of variational inequalities. It implies a new qualitative property of solutions in $W^{1,p}(\Omega )$ which we call "jumping over the control obstacle." Using the Schwarz symmetrization technique, we give an existence and symmetrization theorems in $W_0^{1,p}(\Omega )\cap L^{\infty }(\Omega )$ which agree completely with previous qualitative results. Also we consider generating singularities of weak solutions in $W^{1,p}(\Omega )$ of variational inequalities.
Classification : 35J65, 35J85, 35B05
Keywords: variational inequalities, double obstacle, qualitative properties, Schwarz symmetrization, generating singularities 
@article{EJDE_2002__2002__a188,
     author = {Korkut,  Luka and Pa\v{s}i\'c,  Mervan and \v{Z}ubrini\'c,  Darko},
     title = {A class of nonlinear elliptic variational inequalities: {Qualitative} properties and existence of solutions},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {0991.35037},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a188/}
}
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AU  - Pašić,  Mervan
AU  - Žubrinić,  Darko
TI  - A class of nonlinear elliptic variational inequalities: Qualitative properties and existence of solutions
JO  - Electronic journal of differential equations
PY  - 2002
VL  - 2002
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LA  - en
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%A Pašić,  Mervan
%A Žubrinić,  Darko
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%J Electronic journal of differential equations
%D 2002
%V 2002
%U http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a188/
%G en
%F EJDE_2002__2002__a188
Korkut,  Luka; Pašić,  Mervan; Žubrinić,  Darko. A class of nonlinear elliptic variational inequalities: Qualitative properties and existence of solutions. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a188/