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Boundary Values in the Geometric Function Theory in Domains with Moving Boundaries
This article addresses the problem of boundary correspondence for a sequence of homeomorphisms that change the capacity of a condenser in...
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Free Boundary Problems for Compressible Flows
The macroscopic dynamics of compressible gasses and fluids are well described by the compressible Euler and Navier Stokes equations. In the simplest...
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Endogenous Boundary Value Problems
Continuing the unified approach, we will first solve abstract equations involving a maximal operator of differential quadruplets. Next these...
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On nonminimizing solutions of elliptic free boundary problems
We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily...
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The nonhomogeneous boundary-value problems for the 1D-NLS equation with lineal boundary condition
In this paper, we study the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with different...
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On the Effect of Irregularity of the Domain Boundary on the Solution of a Boundary Value Problem for the Laplace Equation
AbstractWe consider an inhomogeneous boundary value problem with mixed boundary conditions for the Laplace equation in a domain representing a...
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Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial...
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A vectorial problem with thin free boundary
We consider the vectorial analogue of the thin free boundary problem introduced by Caffarelli et al. (J Eur math Soc 12:1151-1179, 2010) as a...
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A New Boundary of the Map** Class Group
Based on the action of the map** class group on the space of measured foliations, we construct a new boundary of the map** class group and study...
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Boundary controllability for a 1D degenerate parabolic equation with drift, a singular potential, and a Neumann boundary condition
We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and a singular potential. Here, we consider a...
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The First Width of Non-negatively Curved Surfaces with Convex Boundary
In this paper, free boundary geodesic networks whose length realizes the first min–max width of the length functional are investigated. This...
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On Some Elliptic Boundary Value Problems in Conic Domains
AbstractA model elliptic pseudodifferential equation in a polyhedral cone is considered, and the situation when some of the parameters of the cone...
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On a boundary property of Blaschke products
A Blaschke product has no radial limits on a subset E of the unit circle T but has unrestricted limit at each point of T \ E if and only if E is a...
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Least gradient problem with Dirichlet condition imposed on a part of the boundary
We provide an analysis of the least gradient problem in the case when the boundary datum is only imposed on a part of the boundary. First, we give a...
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Boundary Regularity of Isometries Between Infinitely Flat Complex Domains
In this paper we prove that isometries with respect to the Kobayashi metric between certain domains having boundary points at which the boundary is...
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Multiplicity one for min–max theory in compact manifolds with boundary and its applications
We prove the multiplicity one theorem for min–max free boundary minimal hypersurfaces in compact manifolds with boundary of dimension between 3 and 7...
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Magnetic Boundary Control I: Graphs with Several Cycles
This is the first chapter devoted to the Magnetic Boundary Control method (MBC-method).