Nonexistence results for parabolic equations involving the p-Laplacian and Hardy–Leray-type inequalities on Riemannian manifolds

  • Yazar/lar GOLDSTEIN, Gisèle Ruiz
    GOLDSTEIN, Jerome Arthur
    KÖMBE, İsmail
    BAKIM, Sümeyye
  • Yayın Türü Makale
  • Yayın Tarihi 2021
  • Tek Biçim Adres http://hdl.handle.net/20.500.12498/5846

The main goal of this paper is twofold. The first one is to investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation on a noncompact Riemannian manifold M, ⎧ ⎪⎨ ⎪⎩ ∂u ∂t = Δp,gu + V(x)u p−1 + λuq in Ω × (0, T ), u(x, 0) = u0(x) ≥ 0 in Ω, u(x, t) = 0 on ∂Ω × (0, T ), where 1 < p < 2, V ∈ L1 loc(Ω), q > 0, λ ∈ R, Ω is bounded and has a smooth boundary in M and Δp,g is the p-Laplacian on M. The second one is to obtain Hardy- and Leray-type inequalities with remainder terms on a Riemannian manifold M that provide us concrete potentials to use in the partial differential equation we are interested in. In particular, we obtain explicit (mostly sharp) constants for these inequalities on the hyperbolic space Hn.

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Eser Adı
(dc.title)
Nonexistence results for parabolic equations involving the p-Laplacian and Hardy–Leray-type inequalities on Riemannian manifolds
Yayın Türü
(dc.type)
Makale
Yazar/lar
(dc.contributor.author)
GOLDSTEIN, Gisèle Ruiz
Yazar/lar
(dc.contributor.author)
GOLDSTEIN, Jerome Arthur
Yazar/lar
(dc.contributor.author)
KÖMBE, İsmail
Yazar/lar
(dc.contributor.author)
BAKIM, Sümeyye
Atıf Dizini
(dc.source.database)
Wos
Atıf Dizini
(dc.source.database)
Scopus
Yayın Tarihi
(dc.date.issued)
2021
Kayıt Giriş Tarihi
(dc.date.accessioned)
2023-02-24T13:13:39Z
Açık Erişim tarihi
(dc.date.available)
2023-02-24T13:13:39Z
Özet
(dc.description.abstract)
The main goal of this paper is twofold. The first one is to investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation on a noncompact Riemannian manifold M, ⎧ ⎪⎨ ⎪⎩ ∂u ∂t = Δp,gu + V(x)u p−1 + λuq in Ω × (0, T ), u(x, 0) = u0(x) ≥ 0 in Ω, u(x, t) = 0 on ∂Ω × (0, T ), where 1 < p < 2, V ∈ L1 loc(Ω), q > 0, λ ∈ R, Ω is bounded and has a smooth boundary in M and Δp,g is the p-Laplacian on M. The second one is to obtain Hardy- and Leray-type inequalities with remainder terms on a Riemannian manifold M that provide us concrete potentials to use in the partial differential equation we are interested in. In particular, we obtain explicit (mostly sharp) constants for these inequalities on the hyperbolic space Hn.
Yayın Dili
(dc.language.iso)
en
Tek Biçim Adres
(dc.identifier.uri)
http://hdl.handle.net/20.500.12498/5846
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