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- W4316830059 abstract "We consider fractional partial differential equations posed on the full space $R^d$. Using the well-known Caffarelli-Silvestre extension to $R^d times R^+$ as equivalent definition, we derive existence and uniqueness of weak solutions. We show that solutions to a truncated extension problem on $R^d times (0,YY)$ converge to the solution of the original problem as $YY rightarrow infty$. Moreover, we also provide an algebraic rate of decay and derive weighted analytic-type regularity estimates for solutions to the truncated problem. These results pave the way for a rigorous analysis of numerical methods for the full space problem, such as FEM-BEM coupling techniques." @default.
- W4316830059 created "2023-01-17" @default.
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- W4316830059 date "2023-01-13" @default.
- W4316830059 modified "2023-10-01" @default.
- W4316830059 title "Fractional Diffusion in the full space: decay and regularity" @default.
- W4316830059 doi "https://doi.org/10.48550/arxiv.2301.05503" @default.
- W4316830059 hasPublicationYear "2023" @default.
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