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• W2093119883 abstract "We introduce a class of weak solutions to the quasilinear equation $-Delta_p u = sigma |u|^{p-2}u$ in an open set $Omegasubsetmathbf{R}^n$. Here $p>1$, and $Delta_p u$ is the $p$-Laplacian operator. Our notion of solution is tailored to general distributional coefficients $sigma$ satisfying a certain weighted Sobolev-Poincare inequality. We also study weak solutions of the closely related equation $-Delta_p v = (p-1)|nabla v|^p + sigma$, under the same conditions on $sigma$. Our results for this latter equation will allow us to characterize the class of distributions $sigma$ which satisfy the Sobolev-Poincare inequality, thereby extending earlier results on the form boundedness problem for the Schrodinger operator to $pneq 2$." @default.
• W2093119883 created "2016-06-24" @default.
• W2093119883 creator A5010456839 @default.
• W2093119883 creator A5036028881 @default.
• W2093119883 creator A5081425165 @default.
• W2093119883 date "2012-04-13" @default.
• W2093119883 modified "2023-10-16" @default.
• W2093119883 title "Quasilinear elliptic equations and weighted Sobolev-Poincar'{e} inequalities with distributional weights" @default.
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• W2093119883 hasPublicationYear "2012" @default.
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