Related papers: On a two-phase problem for harmonic measure in gen…

We show exact dimensionality of harmonic measures associated with random walks on groups acting on a hyperbolic space under finite first moment condition, and establish the dimension formula by the entropy over the drift. We also treat the…

Following Weaver we study generalized differential operators, called (metric) derivations, and their linear algebraic properties. In particular, for k = 1, 2 we show that measures on k-dimensional Euclidean space that induce rank-k modules…

The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled…

The question of unique continuation of harmonic functions in a domain $\Omega$ $\subset$ R d with boundary $\partial$$\Omega$, satisfying Dirichlet boundary conditions and with normal derivatives vanishing on a subset $\omega$ of the…

We prove a regularity theorem for harmonic maps into Teichm\"uller space. More specifically, if $u$ is a harmonic map from a Riemannian domain to the metric completion of Teichm\"uller space with respect to the Weil-Petersson metric, and…

Simultaneous decoherence of conjugate observables of an open quantum system leads to a classical statistical mechanical description with constant phase space probability density in terms of a uniform ensemble. We investigate a scenario…

We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We find conditions…

Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning radius of convergence…

We explore theoretically the physics of a collection of two-level systems coupled to a single-mode bosonic field in the non-standard configuration where each (artificial) atom is coupled to both field quadratures of the boson mode. We…

Via Gauge theory, we give a new proof of partial regularity for harmonic maps in dimension m>2 into arbitrary targets. This proof avoids the use of adapted frames and permits to consider targets of "minimal" C^2 regularity. The proof we…

We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is…

The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…

In this paper, we study the eikonal equation in metric measure spaces, where the inhomogeneous term is allowed to be discontinuous, unbounded and merely $p$-integrable in the domain with a finite $p$. For continuous eikonal equations, it is…

We consider the isoperimetric problem defined on the whole $\mathbb{R}^n$ by the Allen--Cahn energy functional. For non-degenerate double well potentials, we prove sharp quantitative stability inequalities of quadratic type which are…

We consider two disjoint sets of points. If at least one of the sets can be embedded into an Euclidean space, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean…

A condition for the synchronizability of a pair of PDE systems, coupled through a finite set of variables, is commonly the existence of internal synchronization or internal coherence in each system separately. The condition was previously…

Let $\Omega\subset \mathbb{R}^{n+1}$ be an open set, not necessarily connected, with an $n$-dimensional uniformly rectifiable boundary. We show that $\partial\Omega$ may be approximated in a "Big Pieces" sense by boundaries of chord-arc…

We give a sufficient condition for H\"older continuity at a boundary point for quasiminima of double-phase functionals of $p,q$-Laplace type, in the setting of metric measure spaces equipped with a doubling measure and supporting a…

We show the absolute continuity of the spectrum and determine the spectrum as a set for two classes of Hadamard manifolds and for specific domains and quotients of one of the classes.

We investigate trend to equilibrium for the damped wave equation with a confining potential in the Euclidean space. We provide with necessary and sufficient geometric conditions for the energy to decay exponentially uniformly. The proofs…