Related papers: Inequalities in problems on non-overlapping domain…

We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half-spaces.

A linear quadratic Dirichlet control problem posed on a possibly non-convex polygonal domain is analyzed. Detailed regularity results are provided in classical Sobolev (Slobodetskii) spaces. In particular, it is proved that in the presence…

We discuss the problem of possible boundary terms at poles of the drift in the complex Langevin method, which spoil correctness of the method. For the simplest, however paradigmatic cases we can find complete answers. Lessons for more…

We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of…

Which nonlocal correlations can be obtained, when a party has access to more than one subsystem? While traditionally nonlocality deals with spacelike separated parties, this question becomes important with quantum technologies that connect…

This work is an extension of the incomplete probability theory from the simple case of monofractals previously studied to the more general case of multifractals which can occur in the phase space without equiprobable partition.

We prove the existence of infinitely many solutions to a class of non-symmetric Dirichlet problems with exponential nonlinearities. Here the domain $\Omega \subset\subset \mathbb{R}^{2l}$ where $2l$ is the order of the equation. Considered…

We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily minimize energy. As applications, we obtain mountain pass solutions of critical and…

We investigate the count of meromorphic differentials on the Riemann sphere possessing a single zero, multiple poles with prescribed orders, and fixed residues at each pole. Gendron and Tahar previously examined this problem with respect to…

This paper deals with a class of nonlinear elliptic equations involving a critical power-nonlinearity as well as a potential featuring multiple inverse square singularities. When the poles form a symmetric structure, it is natural we wonder…

We prove that bounded solutions to an overdetermined fully nonlinear free boundary problem in the plane are one dimensional. Our proof relies on maximum principle techniques and convexity arguments.

The main purpose of this work is to ascertain when arithmetic operations with periodic functions whose domains may not coincide with the whole real line preserve periodicity.

Laplace problems on planar domains can be solved by means of least-squares expansions associated with polynomial or rational approximations. Here it is shown that, even in the context of an analytic domain with analytic boundary data, the…

It is well known that for a first order system of linear difference equations with rational function coefficients, a solution that is holomorphic in some left half plane can be analytically continued to a meromorphic solution in the whole…

We present a series of recent results on some new classes of free boundary problems. Differently from the classical literature, the problems considered have either a "nonlocal" feature (e.g., the interaction or/and the interfacial energy…

The set of matrix tuples with invariant subspaces whose dimensions sum up to the dimension of the space, but which do not span the whole space form an algebraic hypersurface. We found the equation of this hypersurface. This generalizes…

We investigate the use of non-overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a…

The paper considers the Novikov problem of describing the geometry of level lines of quasi-periodic functions on the plane. We consider here the most general case, when the number of quasi-periods of a function is not limited. The main…

In this paper we give an overview of some recent and older results concerning free boundary problems governed by elliptic operators.

Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in [Ann. Phys. 351, 1-12 (2014)]. The exact solutions of these equations give the number…