Related papers: Evans-Selberg potential on planar domains

This is my master thesis. Unfortunately it is written in Italian, but maybe somebody will find it helpful when it comes to Evans Potentials

We obtain pointwise estimates for solutions of semilinear parabolic equations with a potential on connected domains both of $\mathbb R^n$ and of general Riemannian manifolds.

For a once-punctured complex torus, we compare the Bergman kernel and the fundamental metric, by constructing explicitly the Evans-Selberg potential and discussing its asymptotic behaviors. This work aims to generalize the Suita type…

We provide pointwise upper bounds for the transition kernels of semigroups associated with a class of systems of nondegenerate elliptic partial differential equations with unbounded coefficients with possibly unbounded diffusion…

In this paper, we prove the Evans-Krylov theorem for nonlocal parabolic fully nonlinear equations.

In this paper, we survey and refine several results -- some previously established in the literature -- that facilitate the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We apply…

We present a technique for computing explicit, concrete formulas for the weighted Bergman kernel on a planar domain with weight the modulus squared of a meromorphic function in the case that the meromorphic function has a finite number of…

We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller--Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero.…

We consider a class of parabolic equations with critical electromagnetic potentials, for which we obtain a classification of local asymptotics, unique continuation results, and an integral representation formula for solutions.

We shall give a variational formula of the full Bergman kernels associated to a family of smoothly bounded strongly pseudoconvex domains. An equivalent criterion for the triviality of holomorphic motions of planar domains in terms of the…

We establish H\"older estimates for the time derivative of solutions of non-local parabolic equations under mild assumptions for the boundary data. As a consequence we are able to extend the Evans-Krylov estimate for rough kernels to…

The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…

Estimates of the Bergman kernel and the Bergman and Kobayashi metrics on pseudoconvex domains near boundaries with constant Levi ranks are given.

We consider systems of parabolic linear equations, subject to Neumann boundary conditions on bounded domains in $\mathbb{R}^d$, that are coupled by a matrix-valued potential $V$, and investigate under which conditions each solution to such…

Recently we proposed a generic construction of the additional integrals of motion for the St\"ackel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for…

In this paper second-order elliptic and parabolic partial differential systems are considered on $C^1$ domains. Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the…

In this article, we study some properties of the $n$-th order weighted reduced Bergman kernels for planar domains, $n\geq 1$. Specifically, we look at Ramadanov type theorems, localization, and boundary behaviour of the weighted reduced…

In this work, we generalize Ernst potentials to the Einstein-Maxwell-Dilaton case and explicitly write the corresponding potential space metric. Since this metric is five-dimensional in potential space, we generalize the corresponding…

Given a parabolic geometry, it is sometimes possible to find special metrics characterised by some invariant conditions. In conformal geometry, for example, one asks for an Einstein metric in the conformal class. Einstein metrics have the…

We study Bergman kernels $K_\Pi$ and projections $P_\Pi$ in unbounded planar domains $\Pi$, which are periodic in one dimension. In the case $\Pi$ is simply connected we write the kernel $K_\Pi$ in terms of a Riemann mapping $\varphi$…