Regularity properties of solutions of a class of elliptic-parabolic nonlinear Levi type equations (Q2782665)
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scientific article; zbMATH DE number 1725357
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regularity properties of solutions of a class of elliptic-parabolic nonlinear Levi type equations |
scientific article; zbMATH DE number 1725357 |
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Regularity properties of solutions of a class of elliptic-parabolic nonlinear Levi type equations (English)
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8 April 2002
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freezing method
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Lie groups
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fundamental solutions
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bootstrap argument
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The authors prove the smoothness of solutions of a class of elliptic-parabolic nonlinear Levi type equations, represented as a sum of squares plus a vector field. By means of a freezing method argument they are able to reduce the study of the operator to the study of a family of left invariant operators on a free nilpotent Lie group. Then they use the fundamental solution of the frozen operator as a parametrix for the Levi operator and deduce a representation formula for the solutions of the given equation. After that, differentiating this formula and by using a bootstrap argument they deduce that the solutions are \( C^\infty\).
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