Boundary trace of solutions of semilinear elliptic equalities and inequalities (Q2504958)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Boundary trace of solutions of semilinear elliptic equalities and inequalities |
scientific article |
Statements
Boundary trace of solutions of semilinear elliptic equalities and inequalities (English)
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1 February 2007
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Let \(\Omega\) be a smooth domain in the Euclidean space. This paper is concerned with \(C^1(\Omega )\) solutions of the differential inequality \(\Delta u\leq g(x,u)\) in \(\Omega\), where \(g\) is a continuous real-valued function with super-linear growth. In this paper there are proposed three methods in order to define the boundary trace of positive solutions. Several examples containing various nonlinearities of absorption type illustrate the abstract results of this paper.
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Laplacian
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Poisson potential
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singularities
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Radon measures
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Borel measures
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balayage
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convergence in measures
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