On some nonlinear equation involving the 1-Laplacian and trace map inequalities (Q1348784)
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scientific article; zbMATH DE number 1740684
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some nonlinear equation involving the 1-Laplacian and trace map inequalities |
scientific article; zbMATH DE number 1740684 |
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On some nonlinear equation involving the 1-Laplacian and trace map inequalities (English)
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3 June 2002
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The paper deals with the study of a minimization problem in the Sobolev space \(W^{1,1}(\Omega)\), where \(\Omega\) is a bounded open set in \({\mathbb R}^N\) with smooth boundary. Due to the non-reflexivity of this space, the author obtains the existence of a solution in \(\text{BV}(\Omega)\). The proofs rely on refined and powerful methods specific to the theory of functions of bounded variation.
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minimization problem
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nonlinear differential equation
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bounded variation
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convex analysis
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