Vetenskap & teknik
Pocket
Fundamental Solutions and Local Solvability for Nonsmooth Hormander's Operators
Marco Bramanti • Luca Brandolini • Maria Manfredini • Marco Pedroni
1549:-
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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 Hormander's vector fields of step $r$ such that the highest order commutators are only Holder 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 they deduce the local solvability of $L$, constructing, by means of $\gamma$, a solution to $Lu=f$ with Holder continuous $f$. The authors also prove $C_{X,loc}^{2,\alpha}$ estimates on this solution.
- Format: Pocket/Paperback
- ISBN: 9781470425593
- Språk: Engelska
- Antal sidor: 79
- Utgivningsdatum: 2017-10-30
- Förlag: American Mathematical Society