Given 1<p<N and two measurable functions V(r)≥0 and K(r)>0, r>0, we define the weighted spaces W = {u ∈ D^{1,p}(R^N) : ∫_R^N V(|x|)|u|^p dx < ∞}, L_K^q = L^q(R^N, K(|x|)dx) and study the compact embeddings of the radial subspace of W into L_K^q1+L_K^q2, and thus into L_K^q (=L_K^q+L_K^q) as a particular case. Both exponents q1,q2,q greater and lower than p are considered. Our results do not require any compatibility between how the potentials V and K behave at the origin and at infinity, and essentially rely on power type estimates of their relative growth, not of the potentials separately.

Badiale, M., Guida, M., Rolando, S. (2015). Compactness results for the p-Laplace equation [Working paper].

Compactness results for the p-Laplace equation

ROLANDO, SERGIO
2015

Abstract

Given 10, r>0, we define the weighted spaces W = {u ∈ D^{1,p}(R^N) : ∫_R^N V(|x|)|u|^p dx < ∞}, L_K^q = L^q(R^N, K(|x|)dx) and study the compact embeddings of the radial subspace of W into L_K^q1+L_K^q2, and thus into L_K^q (=L_K^q+L_K^q) as a particular case. Both exponents q1,q2,q greater and lower than p are considered. Our results do not require any compatibility between how the potentials V and K behave at the origin and at infinity, and essentially rely on power type estimates of their relative growth, not of the potentials separately.
Working paper
Scientifica
Weighted Sobolev spaces, compact embeddings, unbounded or decaying potentials
English
Badiale, M., Guida, M., Rolando, S. (2015). Compactness results for the p-Laplace equation [Working paper].
Badiale, M; Guida, M; Rolando, S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/106681
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