Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces
By Ariel Barton, Svitlana Mayboroda. 2013
53 citations recorded by the source corpus.
This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Sobolev classes. We establish mapping properties for the double and single layer potentials, as well as the Newton potential, on Besov spaces. We prove extrapolation-type solvability results: that is, we show that solvability of the Dirichlet or Neumann boundary value problem at any given L^p space automatically assures their solvability in an extended range of Besov spaces. We also establish well-posedness for non-homogeneous boundary value problems. In particular, we prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric coefficients.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/39d53215bb1e4733ed7c16ebed1acf6d1bed4516
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In Applied Mathematics
- M. Mitrea
- S. Hofmann
- Andrew J. Morris
- P. Auscher
- J. M. Martell
- Svitlana Mayboroda
- A. Mcintosh
- Xuan Thinh Duong
In Mathematical Physics
Citations in the corpus
- The method of layer potentials in Lp and endpoint spaces for elliptic operators with L∞ coefficients (2013, methodology): “ (R n+1 + ), if β= 0, or u ∈ C˙β(Rn), if β>0). We refer the reader to [28] for a proof of the uniqueness for (N)p, (R)p and (D)q for a more general class of operators. Also, we refer the reader to [10] for a proof of the uniqueness for (D)Λβ in the case β>0. Finally, the uniqueness for (D)Λ0 =”
- The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients (2013, unknown): “mpat ible solvability right after it). Note, in particular, our comments regarding the sense of the convergence to the boundary data in the introduction to the present manuscript. Then Remark 9.15 in [BM] detailed the passage from compatible solvability to the well-posedness. REGULARITY PROBLEM 31 T”