Given two measurable functions (Formula presented.) we define the weighted spaces (Formula presented.) and study the compact embeddings of the radial subspace of (Formula presented.) q 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. Applications to existence results for nonlinear elliptic problems like (Formula presented.) will be given in a forthcoming paper.

Badiale, M., Guida, M., Rolando, S. (2015). Compactness and existence results in weighted Sobolev spaces of radial functions. Part I: compactness. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 54(1), 1061-1090 [10.1007/s00526-015-0817-2].

Compactness and existence results in weighted Sobolev spaces of radial functions. Part I: compactness

ROLANDO, SERGIO
2015

Abstract

Given two measurable functions (Formula presented.) we define the weighted spaces (Formula presented.) and study the compact embeddings of the radial subspace of (Formula presented.) q 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. Applications to existence results for nonlinear elliptic problems like (Formula presented.) will be given in a forthcoming paper.
Articolo in rivista - Articolo scientifico
Weighted Sobolev spaces, compact embeddings, unbounded or decaying potentials
English
1061
1090
30
Badiale, M., Guida, M., Rolando, S. (2015). Compactness and existence results in weighted Sobolev spaces of radial functions. Part I: compactness. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 54(1), 1061-1090 [10.1007/s00526-015-0817-2].
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/10281/106666
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