Geodesic
Nonexistence of solutions for quasilinear elliptic equations with \(p\)-growth in the gradient
Electronic journal of differential equations, Tome 2002 (2002)
We study the nonexistence of weak solutions in $W^{1,p}_{{\rm loc}}(\Omega)$ for a class of quasilinear elliptic boundary-value problems with natural growth in the gradient. Nonsolvability conditions involve general domains with possible singularities of the right-hand side. In particular, we show that if the data on the right-hand side are sufficiently large, or if inner radius of $\Omega$ is large, then there are no weak solutions.
Classification : 35J25, 35J60, 45J05
Keywords: quasilinear elliptic, existence, nonexistence, geometry of domains 
@article{EJDE_2002__2002__a66,
     author = {\v{Z}ubrini\'c,  Darko},
     title = {Nonexistence of solutions for quasilinear elliptic equations with \(p\)-growth in the gradient},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1068.35509},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a66/}
}
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TI  - Nonexistence of solutions for quasilinear elliptic equations with \(p\)-growth in the gradient
JO  - Electronic journal of differential equations
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VL  - 2002
UR  - http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a66/
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%A Žubrinić,  Darko
%T Nonexistence of solutions for quasilinear elliptic equations with \(p\)-growth in the gradient
%J Electronic journal of differential equations
%D 2002
%V 2002
%U http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a66/
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%F EJDE_2002__2002__a66
Žubrinić,  Darko. Nonexistence of solutions for quasilinear elliptic equations with \(p\)-growth in the gradient. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a66/