Geodesic
Nonexistence of solutions for quasilinear elliptic equations with $p$-growth in the gradient
Electronic Journal of Differential Equations, Tome 2002 (2002).

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

Summary: 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__a266,
     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},
     publisher = {mathdoc},
     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a266/}
}
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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__a266/