The aim of this work is to prove a compact embedding for weighted fractional Sobolev spaces. As an application, we use this embedding to prove, via variational methods, the existence of solutions to the following Schrödinger equation (Formula presented.) where the two measurable functions K>0 and (Formula presented.) could vanish at infinity.
Bernini, F., Rolando, S., Secchi, S. (2026). Compact embeddings for weighted fractional Sobolev spaces and applications to nonlinear Schrödinger equations. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 1-29 [10.1080/17476933.2026.2626782].
Compact embeddings for weighted fractional Sobolev spaces and applications to nonlinear Schrödinger equations
Bernini F.
;Rolando S.;Secchi S.
2026
Abstract
The aim of this work is to prove a compact embedding for weighted fractional Sobolev spaces. As an application, we use this embedding to prove, via variational methods, the existence of solutions to the following Schrödinger equation (Formula presented.) where the two measurable functions K>0 and (Formula presented.) could vanish at infinity.
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