Related papers: Some remarks on uniform boundary Harnack Principle…
We consider a Hamiltonian system of free boundary type, showing first uniform bounds and existence of solutions and of the free boundary. Then, for any smooth and bounded domain, we prove uniqueness of positive solutions in a suitable…
We study the Hamiltonian dynamics of a charged particle submitted to a pure magnetic field in a two-dimensional domain. We provide conditions on the magnetic field in a neighbourhood of the boundary to ensure the confinement of the…
Learning guarantees often rely on assumptions of i.i.d. data, which will likely be violated in practice once predictors are deployed to perform real-world tasks. Domain adaptation approaches thus appeared as a useful framework yielding…
The purpose of this note is to use the scaling principle to study the boundary behaviour of some conformal invariants on planar domains. The focus is on the Aumann--Carath\'{e}odory rigidity constant, the higher order curvatures of the…
We show how the (globally supersymmetric) model of Mirabelli and Peskin can be formulated in the boundary (``downstairs'' or ``interval'') picture. The necessary Gibbons-Hawking-like terms appear naturally when using (codimension one)…
We study the effect of domain perturbation on invariant manifolds for semilinear parabolic equations subject to Dirichlet boundary condition. Under Mosco convergence assumption on the domains, we prove the upper and lower semicontinuity of…
We study two special cases of the planar least gradient problem. In the first one, the boundary conditions are imposed on a part of the strictly convex domain. In the second case, we impose the Dirichlet data on the boundary of a rectangle,…
In this paper, we look at a linear system of ordinary differential equations as derived from the two-dimensional Ginzburg-Landau equation. In two cases, it is known that this system admits bounded solutions coming from the invariance of the…
We investigate the orientation of nonlinear stripe patterns in finite domains. Motivated by recent experiments, we introduce a control parameter drop from supercritical inside a domain to subcritical outside without boundary conditions at…
We prove well posedness and stability in $\mathbf{L}^1$ for a class of mixed hyperbolic-parabolic non linear and non local equations in a bounded domain with no flow along the boundary. While the treatment of boundary conditions for the…
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence,…
In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems,…
This paper concerns the boundary behavior of solutions of certain fully nonlinear equations with a general drift term. We elaborate on the non-homogeneous generalized Harnack inequality proved by the second author in (Julin, ARMA -15), to…
In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…
The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle…
The Hot Spots constant for bounded smooth domains was recently introduced by Steinerberger (2021) as a means to control the global extrema of the first nontrivial eigenfunction of the Neumann Laplacian by its boundary extrema. We generalize…
The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only…
We provide some versions of the Zaremba-Hopf-Oleinik boundary point lemma for general elliptic and parabolic equations in divergence form under the sharp requirements on the coefficients of equations and on the boundaries of domains.
A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.