On the $\mathrm{L}^p$-theory for second-order elliptic operators in divergence form with complex coefficients
| Autor: | ter Elst, A. F. M., Haller-Dintelmann, R., Rehberg, J., Tolksdorf, P. |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given a complex, elliptic coefficient function we investigate for which values of $p$ the corresponding second-order divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly continuous semigroup on $\mathrm{L}^p(\Omega)$. Additional properties like analyticity of the semigroup, $\mathrm{H}^\infty$-calculus and maximal regularity are also discussed. Finally we prove a perturbation result for real coefficients that gives the whole range of $p$'s for small imaginary parts of the coefficients. Our results are based on the recent notion of $p$-ellipticity, reverse H\"older inequalities and Gaussian estimates for the real coefficients. Comment: 37 pages |
| Databáze: | arXiv |
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