The role of fundamental solution in Potential and Regularity Theory for subelliptic PDE
| Autor: | Maria Manfredini, Giovanna Citti, Andrea Bonfiglioli, Daniele Morbidelli, Giovanni Cupini, Andrea Pascucci, Sergio Polidoro, Francesco Uguzzoni, Annamaria Montanari |
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| Přispěvatelé: | Giovanna Citti, Maria Manfredini, Daniele Morbidelli, Sergio Polidoro, Francesco Uguzzoni, Bonfiglioli, Andrea, Citti, Giovanna, Cupini, Giovanni, Manfredini, Maria, Montanari, Annamaria, Morbidelli, Daniele, Pascucci, Andrea, Uguzzoni, Francesco, Polidoro Sergio |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Parametrix
Fundamental solution Subelliptic operator Differential equation Subelliptic PDEs Mathematical analysis Explained sum of squares Boundary (topology) Potential theory Hormander operators Poincare inequality Kernel (linear algebra) Operator (computer programming) Fundamental solution Mathematics |
| Zdroj: | Geometric Methods in PDE’s ISBN: 9783319026657 |
| Popis: | In this survey we consider a general Hormander type operator, represented as a sum of squares of vector fields plus a drift and we outline the central role of the fundamental solution in developing Potential and Regularity Theory for solutions of related PDEs. After recalling the Gaussian behavior at infinity of the kernel, we show some mean value formula on the level set of the fundamental solution, which allow to obtain a comprehensive parallel of the classical Potential Theory. Then we show that a precise knowledge of the fundamental solution leads to global regularity results: estimates at the boundary or on the whole space. Finally in the problem of regularity of non linear differential equations we need an ad hoc modification of the parametrix method, based on the properties of the fundamental solution of an approximating problem. |
| Databáze: | OpenAIRE |
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