Trace inequalities of the Sobolev type and nonlinear Dirichlet problems

Hara, Takanobu

Trace inequalities of the Sobolev type and nonlinear Dirichlet problems

Hara, Takanobu

Calculus of Variations and Partial Differential Equations, 2022, 61(6), 216

Permalink : https://hdl.handle.net/2115/90525

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アクセス権	open access
URI	https://hdl.handle.net/2115/90525
タイトル	Trace inequalities of the Sobolev type and nonlinear Dirichlet problems
著者	著者名 Hara, Takanobu
言語	英語
キーワード	Quasilinear elliptic equation
	p-Laplacian
	Measure data
	Trace in-equality
	Singular elliptic equations
発行日	2022-10-08
出版者	Springer
収録物名	Calculus of Variations and Partial Differential Equations
巻(号)	61(6)
ページ	216
抄録	We discuss the solvability of nonlinear Dirichlet problems of the type −Δp,wu=σ in Ω; u=0 on ∂Ω, where Ω is a bounded domain in Rn, Δp,w is a weighted (p, w)-Laplacian and σ is a nonnegative locally finite Radon measure on Ω. We do not assume the finiteness of σ(Ω). We revisit this problem from a potential theoretic perspective and provide criteria for the existence of solutions by Lp(w)−Lq(σ) trace inequalities or capacitary conditions. Additionally, we apply the method to the singular elliptic problem −Δp,wu=σu−γ in Ω; u=0 on ∂Ω and derive connection with the trace inequalities.
資源タイプ	学術雑誌論文
出版タイプ	Accepted Manuscript
権利情報	This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00526-022-02339-9
PISSN	0944-2669
EISSN	1432-0835
関連情報 (isVersionOf)	出版社版DOI https://doi.org/10.1007/s00526-022-02339-9