Boundary Value Problems for Elliptic Systems on Weighted Morrey Spaces in Rough Domains

M. Laurel () and M. Mitrea ()
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M. Laurel: Baylor University
M. Mitrea: Baylor University

Chapter Chapter 16 in Integral Methods in Science and Engineering, 2023, pp 191-203 from Springer

Abstract: Abstract The goal of this paper is to present solvability results for boundary value problems for weakly elliptic, homogeneous, constant complex coefficient, second-order systems in Ahlfors regular domains with a sufficiently “flat” boundary (measured in terms of the BMO seminorm of the outward unit normal). The boundary data are arbitrarily prescribed in Muckenhoupt weighted Morrey spaces, and a nontangential maximal function estimate is sought for the solution. Our approach relies on boundary layer potentials. Of particular import is an extrapolation result, which allows us to develop a Calderón-Zygmund theory at the level of weighted Morrey spaces from progress already made concerning singular integral operators (SIO) on Muckenhoupt weighted Lebesgue spaces. We also develop a functional analytic framework and a Calderón-Zygmund theory for SIO acting on the preduals of Morrey spaces, the so called “block spaces.”

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-34099-4_16

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DOI: 10.1007/978-3-031-34099-4_16

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