Related papers: On simpliciality of function spaces not containing…

We consider the boundary value problem associated to the curl operator, with vanishing Dirichlet boundary conditions. We prove, under mild regularity of the data of the problem, existence of classical solutions.

We prove some new log-free density theorems for zeros of Dirichlet L-functions (which accordingly are more sharp than earlier ones near to the boundary line of the critical strip). The results can be applied in several problems of prime…

We present explicit formulas for solutions to nonhomogeneous boundary value problems involving any positive power of the Laplacian in the half-space. For non-integer powers the operator becomes nonlocal and this requires a suitable…

We consider positive solutions of a fractional Lane-Emden type problem in a bounded domain with Dirichlet conditions. We show that uniqueness and nondegeneracy hold for the asymptotically linear problem in general domains. Furthermore, we…

In a universe whose elementary constituents are point particles there does not seem to be any obvious mechanism for avoiding the initial singularities in physical quantities in the standard model of cosmology. In contrast in string theory…

In this paper we prove the existence and uniqueness of positive classical solution of the fractional Laplacian with singular nonlinearity in a smooth bounded domain with zero Drichlet boundary conditions. By the method of sub-supersolution,…

We study a Dirichlet boundary problem related to the fractional Laplacian in a manifold. Its variational formulation arises in the study of magnitude, an invariant of compact metric spaces given by the reciprocal of the ground state energy.…

We point out that spacetime singularities play a useful role in gravitational theories by eliminating unphysical solutions. In particular, we argue that any modification of general relativity which is completely nonsingular cannot have a…

We develop a framework for studying variational problems in Banach spaces with respect to gradient relations, which encompasses many of the notions of generalized gradients that appear in the literature. We stress the fact that our approach…

Let $\xi$ be a value, at an algebraic point, of a Siegel $E$-function. As a special case of a very general interpolation result, we prove that there exists an $E$-function $f$ such that $f(1)=\xi$, and such that 1 is not a singularity of…

The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…

This paper investigates the Dirichlet problem for a non-divergence form elliptic operator $L$ in a bounded domain of $\mathbb{R}^d$. Under certain conditions on the coefficients of $L$, we first establish the existence of a unique Green's…

We assume that the points in volumes smaller than an elementary volume (which may have a Planck size) are indistinguishable in any physical experiment. This naturally leads to a picture of a discrete space with a finite number of degrees of…

We derive new formulas for the fundamental solutions of slow, viscous flow, governed by the Stokes equations, in a half-space. They are simpler than the classical representations obtained by Blake and collaborators, and can be efficiently…

We present a simple analytic proof that L-functions of real non-principal Dirichlet characters are nonzero at 1.

We provide a simple, unified proof of Birkhoff's theorem for the vacuum and cosmological constant case, emphasizing its local nature. We discuss its implications for the maximal analytic extensions of Schwarzschild, Schwarzschild(-anti)-de…

A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…

In this oaper, we prove some fixed point theorems in metric vector spaces, in which the continuity is not required for the considered mappings to satisfy. We provide some concrete examples to demonstrate these theorems. We also give some…

In this lecture we will show some properties of a singularity-free solution to Einstein's equations and its accordance with some theorems dealing with singularities. We will also discuss the implications of the results.

We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…