January/February 2017 Mixed boundary value problems on cylindrical domains
Pascal Auscher, Moritz Egert
Adv. Differential Equations 22(1/2): 101-168 (January/February 2017). DOI: 10.57262/ade/1484881287

Abstract

We study second-order divergence-form systems on half-infinite cylindrical domains with a bounded and possibly rough base, subject to homogeneous mixed boundary conditions on the lateral boundary and square integrable Dirichlet, Neumann, or regularity data on the cylinder base. Assuming that the coefficients $A$ are close to coefficients $A_0$ that are independent of the unbounded direction with respect to the modified Carleson norm of Dahlberg, we prove a priori estimates and establish well-posedness if $A_0$ has a special structure. We obtain a complete characterization of weak solutions whose gradient either has an $L^2$-bounded non-tangential maximal function or satisfies a Lusin area bound. To this end, we combine the first-order approach to elliptic systems with the Kato square root estimate for operators with mixed boundary conditions.

Citation

Download Citation

Pascal Auscher. Moritz Egert. "Mixed boundary value problems on cylindrical domains." Adv. Differential Equations 22 (1/2) 101 - 168, January/February 2017. https://doi.org/10.57262/ade/1484881287

Information

Published: January/February 2017
First available in Project Euclid: 20 January 2017

zbMATH: 1364.35090
MathSciNet: MR3599513
Digital Object Identifier: 10.57262/ade/1484881287

Subjects:
Primary: 35J55 , 42B25 , 47A60

Rights: Copyright © 2017 Khayyam Publishing, Inc.

Vol.22 • No. 1/2 • January/February 2017
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