| Description |
1 online resource (v, 79 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; number 1182 |
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Memoirs of the American Mathematical Society ; no. 1182.
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| Contents |
Introduction -- Some known results about nonsmooth Hörmander's vector fields -- Geometric estimates -- The parametrix method -- Further regularity of the fundamental solution and local solvability of L -- Appendix: Examples of nonsmooth Hörmander's operators satisfying assumptions A or B -- Bibliography |
| Summary |
The authors consider operators of the form L=\sum_{i=1}̂{n}X_{i}̂{2}+X_{0} in a bounded domain of \mathbb{R}̂{p} where X_{0}, X_{1}, \ldots, X_{n} are nonsmooth Hörmander's vector fields of step r such that the highest order commutators are only Hölder continuous. Applying Levi's parametrix method the authors construct a local fundamental solution \gamma for L and provide growth estimates for \gamma and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients the authors prove that \gamma also possesses second derivatives, and the |
| Notes |
"Volume 249, Number 1182 (third of 8 numbers), September 2017." |
| Bibliography |
Includes bibliographical references (pages 77-79) |
| Notes |
Print version record |
| Subject |
Differential operators.
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Nonsmooth optimization.
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Vector fields.
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Differential operators
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Nonsmooth optimization
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Vector fields
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| Form |
Electronic book
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| Author |
Brandolini, Luca, 1963- author.
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Manfredini, Maria, 1967- author.
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Pedroni, Marco, 1964- author.
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American Mathematical Society, publisher
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| ISBN |
9781470441319 |
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1470441314 |
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