Related papers: Evans-Selberg potential on planar domains

The aim of this paper is to derive on the basis of the Euler's formula several analytical relations which hold for certain classes of planar graphs and which can be useful in algorithmic graph theory.

We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the…

In this paper, we demonstrate the existence of positive solutions for certain weakly coupled elliptic systems of sublinear growth under homogeneous Dirichlet boundary conditions. Our findings generalize existing results related to sublinear…

We solved the problem of the best rational approximation of the Bergman kernels on the unit circle of the complex plane in the quadratic and uniform metrics.

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

In the present work we establish a quantization result for the angular part of the energy of solu- tions to elliptic linear systems of Schr\"odinger type with antisymmetric potentials in two dimension. This quantization is a consequence of…

This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…

We give the parameter version of localization theorem for Bergman metric near the boundary points of strictly pseudoconvex domains. The approximation theorem for square integrable holomorphic functions on such domains in the spirit of…

We study gauge theories based on abelian $p-$ forms on real compact hyperbolic manifolds. The tensor kernel trace formula and the spectral functions associated with free generalized gauge fields are analyzed.

In this study, the Schrodinger equation of a valence electron in a periodic crystal potential is formulated and solved using the elliptic function formalism. The method allows double periodic lattice planes to be represented in the Gauss…

General relations for electromagnetic field energy outside the transparency domain are proposed. It is shown that charged particle contribution to the energy of electromagnetic perturbations in the general case can be described in terms of…

We introduce a notion of quasilinear parabolic equations over metric measure spaces. Under sharp structural conditions, we prove that local weak solutions are locally bounded and satisfy the parabolic Harnack inequality. Applications…

We study large deviations for some non-local parabolic type equations. We show that, under some assumptions on the non-local term, problems defined in a bounded domain converge with an exponential rate to the solution of the problem defined…

In this paper, weighted Bergman spaces on the unit ball in C^n are investigated. A characterization of the Carleson embeddings is established. Pointwise and norm estimates on the reproducing kernel function of weighted Bergman spaces on the…

This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlations of CMB data, using the hybrid approach employed previously: pixel-based at $\ell<30$ and a Gaussian approximation to the distribution of…

Using some nonlinear domain decomposition method, we prove the existence of singular limits for solution of semilinear elliptic problems with exponential nonlinearity.

A set of four scalar conditions involving normal components of the fields D and B and their normal derivatives at a planar surface is introduced, among which different pairs can be chosen to represent possible boundary conditions for the…

We consider a Fokker-Planck operator with electric potential and electromagnetic fields. We establish the sharp weighted and subelliptic estimates, involving the control of the derivatives of electric potential and electromagnetic fields.…

Several aspects of the internal structure of pseudoscalar mesons, accessible through generalized parton distributions in their zero-skewness limit, are examined. These include electromagnetic and gravitational form factors related to charge…

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…