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  • A compact embedding result for anisotropic Sobolev spaces associated to a strip-like domain and some applications
    Alves, Claudianor Oliveira ; Molica Bisci, Giovanni, 1975-
    Let ▫$m \ge 1$▫ and ▫$d \ge 2$▫ be integers and consider a strip-like domain ▫$\mathcal{O} \times \mathbb{R}^d$▫, where ▫$\mathcal{O} \subset \mathbb{R}^m$▫ is a bounded Euclidean domain with smooth ... boundary. Furthermore, let ▫$p \colon \hat{\mathcal{O}} \times \mathbb{R}^d \to \mathbb{R}$▫ be a uniformly continuous and cylindrically symmetric function. We prove that the subspace of ▫$W^{1, p(x,y)} (\mathcal{O} \times \mathbb{R}^d)$▫ consisting of the cylindrically symmetric functions is compactly embedded into ▫$L^\infty (\mathcal{O} \times \mathbb{R}^d)$▫ provided that ▫$$m+d < p_{-} := \inf_{(x,y) \in\hat{\mathcal{O}} \times \mathbb{R}^d} p(x,y) \le p_{+} := \sup_{(x,y) \in\hat{\mathcal{O}} \times \mathbb{R}^d} p(x,y) < +\infty.$$▫ As an application, we study a Neumann problem involving the ▫$p(x,y)$▫-Laplacian operator and an oscillating nonlinearity, proving the existence of infinitely many cylindrically symmetric weak solutions. Our approach is based on variational and topological methods in addition to the principle of symmetric criticality.
    Vir: Journal of mathematical analysis and applications. - ISSN 0022-247X (Vol. 501, iss. 1, Sep. 2021, art. 123490 (24 str.))
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2021
    Jezik - angleški
    COBISS.SI-ID - 18725977

    Povezava(-e):

    https://www.sciencedirect.com/science/article/pii/S0022247X19307589
    DOI

vir: Journal of mathematical analysis and applications. - ISSN 0022-247X (Vol. 501, iss. 1, Sep. 2021, art. 123490 (24 str.))
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