Mean value formulas for classical solutions to subelliptic evolution equations in stratified Lie groups
| Autor: | Pallara, Diego, Polidoro, Sergio |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove mean value formulas for classical solutions to second order linear differential equations in the form $$ \partial_t u = \sum_{i,j=1}^m X_i (a_{ij} X_j u) + X_0 u + f, $$ where $A = (a_{ij})_{i,j=1, \dots,m}$ is a bounded, symmetric and uniformly positive matrix with $C^1$ coefficients under the assumption that the operator $\sum_{j=1}^m X_j^2 + X_0 - \partial_t$ is hypoelliptic and the vector fields $X_1, \dots, X_m$ and $X_{m+1} :=X_0 - \partial_t$ are invariant with respect to a suitable homogeneous Lie group. Our results apply e.g. to degenerate Kolmogorov operators and parabolic equations on Carnot groups $\partial_t u = \sum_{i,j=1}^m X_i (a_{ij} X_j u) + f$. Comment: 29 pages, 2 figures |
| Databáze: | arXiv |
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