Advances in Differential Equations
- Adv. Differential Equations
- Volume 22, Number 1/2 (2017), 101-168.
Mixed boundary value problems on cylindrical domains
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.
Adv. Differential Equations, Volume 22, Number 1/2 (2017), 101-168.
First available in Project Euclid: 20 January 2017
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Auscher, Pascal; Egert, Moritz. Mixed boundary value problems on cylindrical domains. Adv. Differential Equations 22 (2017), no. 1/2, 101--168. https://projecteuclid.org/euclid.ade/1484881287