|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Information Science and Technology / Faculty of Information Science and Technology >
Peer-reviewed Journal Articles, etc >
Trace inequalities of the Sobolev type and nonlinear Dirichlet problems
| Title: | Trace inequalities of the Sobolev type and nonlinear Dirichlet problems |
| Authors: | Hara, Takanobu Browse this author |
| Keywords: | Quasilinear elliptic equation | | p-Laplacian | | Measure data | | Trace in-equality | | Singular elliptic equations |
| Issue Date: | 8-Oct-2022 |
| Publisher: | Springer |
| Journal Title: | Calculus of Variations and Partial Differential Equations |
| Volume: | 61 |
| Issue: | 6 |
| Start Page: | 216 |
| Publisher DOI: | 10.1007/s00526-022-02339-9 |
| Abstract: | 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. |
| Rights: | 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 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/90525 |
| Appears in Collections: | 情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
|
Submitter: 原 宇信
|
