Nonexistence of positive very weak solutions to an elliptic problem with boundary reactions
-
- Takahashi Futoshi
- Department of Mathematics Osaka City University
説明
We consider a semilinear elliptic problem with the boundary reaction:<br>−Δu = 0 in Ω, $\frac{\partial u}{\partial \nu}$ + u = a(x) up + f(x) on ∂Ω,<br>where Ω ⊂ RN, N ≥ 3, is a smooth bounded domain with a flat boundary portion, p > 1, a, f ∈ L1(∂Ω) are nonnegative functions, not identically equal to zero. We provide a necessary condition and a sufficient condition for the existence of positive very weak solutions of the problem. As a corollary, under some assumption of the potential function a, we prove that the problem has no positive solution for any nonnegative external force f ∈ L∞(∂Ω), f $\not\equiv$ 0, even in the very weak sense.
収録刊行物
-
- KODAI MATHEMATICAL JOURNAL
-
KODAI MATHEMATICAL JOURNAL 37 (3), 755-768, 2014
国立大学法人 東京工業大学理学院数学系
- Tweet
詳細情報 詳細情報について
-
- CRID
- 1390001205274464896
-
- NII論文ID
- 130004705923
-
- ISSN
- 18815472
- 03865991
-
- 本文言語コード
- en
-
- データソース種別
-
- JaLC
- Crossref
- CiNii Articles
-
- 抄録ライセンスフラグ
- 使用不可