The Dirichlet Problem for Lévy-stable operators with $L^2$-data
Grube F, Hensiek T, Schefer W (2023)
Calculus of Variations and Partial Differential Equations 63(3): 74.
Zeitschriftenaufsatz
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Abstract / Bemerkung
We prove Sobolev regularity for distributional solutions to the Dirichlet
problem for generators of $2s$-stable processes and exterior data,
inhomogeneity in weighted $L^2$-spaces. This class of operators includes the
fractional Laplacian. For these rough exterior data the theory of weak
variational solutions is not applicable. Our regularity estimate is robust in
the limit $s\to 1-$ which allows us to recover the local theory.
Erscheinungsjahr
2023
Zeitschriftentitel
Calculus of Variations and Partial Differential Equations
Band
63
Ausgabe
3
Art.-Nr.
74
ISSN
0944-2669
eISSN
1432-0835
Page URI
https://pub.uni-bielefeld.de/record/2981299
Zitieren
Grube F, Hensiek T, Schefer W. The Dirichlet Problem for Lévy-stable operators with $L^2$-data. Calculus of Variations and Partial Differential Equations . 2023;63(3): 74.
Grube, F., Hensiek, T., & Schefer, W. (2023). The Dirichlet Problem for Lévy-stable operators with $L^2$-data. Calculus of Variations and Partial Differential Equations , 63(3), 74. https://doi.org/10.1007/s00526-024-02679-8
Grube, Florian, Hensiek, Thorben, and Schefer, Waldemar. 2023. “The Dirichlet Problem for Lévy-stable operators with $L^2$-data”. Calculus of Variations and Partial Differential Equations 63 (3): 74.
Grube, F., Hensiek, T., and Schefer, W. (2023). The Dirichlet Problem for Lévy-stable operators with $L^2$-data. Calculus of Variations and Partial Differential Equations 63:74.
Grube, F., Hensiek, T., & Schefer, W., 2023. The Dirichlet Problem for Lévy-stable operators with $L^2$-data. Calculus of Variations and Partial Differential Equations , 63(3): 74.
F. Grube, T. Hensiek, and W. Schefer, “The Dirichlet Problem for Lévy-stable operators with $L^2$-data”, Calculus of Variations and Partial Differential Equations , vol. 63, 2023, : 74.
Grube, F., Hensiek, T., Schefer, W.: The Dirichlet Problem for Lévy-stable operators with $L^2$-data. Calculus of Variations and Partial Differential Equations . 63, : 74 (2023).
Grube, Florian, Hensiek, Thorben, and Schefer, Waldemar. “The Dirichlet Problem for Lévy-stable operators with $L^2$-data”. Calculus of Variations and Partial Differential Equations 63.3 (2023): 74.
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