The \(C^{\alpha}\) regularity of weak solutions of ultraparabolic equations (Q632366)
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scientific article; zbMATH DE number 5866086
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The \(C^{\alpha}\) regularity of weak solutions of ultraparabolic equations |
scientific article; zbMATH DE number 5866086 |
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The \(C^{\alpha}\) regularity of weak solutions of ultraparabolic equations (English)
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15 March 2011
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The authors consider a class of ultraparabolic equations with measurable coefficients of the form \[ \partial_t \, u= \sum_{i,j=1}^{m_0}X_i(a_{ij}(x,t)X_j\, u )+X_0 u. \] By choosing a new cut-off function, they prove the \(C^{\alpha}\) continuity of weak solutions extending analogous results proved by Lanconelli, Kogoj, Pascucci, Bonfiglioli, Uguzzoni and Polidoro. Their technique is based on a Poincare type inequality and a Harnack type estimate.
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hypoelliptic
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ultraparabolic
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\(C^{\alpha}\) regularity
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