On first and second order planar elliptic equations with degeneracies (Q2882486)
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scientific article; zbMATH DE number 6031005
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On first and second order planar elliptic equations with degeneracies |
scientific article; zbMATH DE number 6031005 |
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On first and second order planar elliptic equations with degeneracies (English)
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6 May 2012
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degenerate elliptic
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spectral values
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fundamental matrix
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asymptotic behavior
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kernels
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semilinear
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normalization
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vector fields
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In this monograph, the author studies the properties of solutions of first and second order equations in the plane. These equations are generated by a complex vector field \(X\) that is elliptic everywhere except along a simple closed curve. The technique used by the author consists to give a thorough study of the operator \(\mathcal{L}\) defined by a unique vector field conjugated to \(X\). The main properties of solutions to \(\mathcal{L}u=0\) or the nonhomogeneous equation are established in a neighborhood of the degeneracy curve through integral and series representations. An application to a class of second order elliptic operators with punctual singularity is given.
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