Related papers: Busemann functions and barrier functions

We study the well-posedness of Hamilton-Jacobi-Bellman equations on subsets of $\mathbb{R}^d$ in a context without boundary conditions. The Hamiltonian is given as the supremum over two parts: an internal Hamiltonian depending on an…

This is the first of a series of two papers which studies the fractional porous medium equation on a Riemannian manifold with isolated conical singularities. In this article, we show $R$-sectoriality for the fractional powers of possibly…

We introduce a new geometric approach to a manifold equipped with a smooth density function that takes a torsion-free affine connection, as opposed to a weighted measure or Laplacian, as the fundamental object of study. The connection…

We give simple and unified proofs of weak holomorhpic Morse inequalities on complete manifolds, $q$-convex manifolds, pseudoconvex domains, weakly $1$-complete manifolds and covering manifolds. This paper is essentially based on the…

We consider planar directed last-passage percolation on the square lattice with general i.i.d. weights and study the geometry of the full set of semi-infinite geodesics in a typical realization of the random environment. The structure of…

We study decay and compact support properties of positive and bounded solutions of $\Delta_{p} u \geq \Lambda(u)$ on the exterior of a compact set of a complete manifold with rotationally symmetry. In the same setting, we also give a new…

We establish a gluing theorem for solutions of a Yamabe problem for manifolds with boundary studied by Escobar in the 90's. Given two scalar-flat Riemannian manifolds whose boundary has zero mean curvature and sharing a submanifold $K$, we…

We prove concavity properties for solutions to anisotropic quasi-linear equations, extending previous results known in the Euclidean case. We focus the attention on nonsmooth anisotropies and in particular we also allow the functions…

We prove that a Riemannian submersion between smooth, compact, non-negatively curved Riemannian manifolds has to be smooth, resolving a conjecture by Berestovskii--Guijarro. We show that without any curvature assumption, the smoothness of…

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…

We construct continuous families of Riemannian metrics on certain simply connected manifolds with the property that the resulting Riemannian manifolds are pairwise isospectral for the Laplace operator acting on functions. These are the…

In this paper we analyse the structure of the spaces of smooth type functions, generated by elements of arbitrary Hilbert spaces, as a continuation of the research in our previous papers in this series. We prove that these spaces are…

We are interested in regularity properties of semi-stable solutions for a class of singular semilinear elliptic problems with advection term defined on a smooth bounded domain of a complete Riemannian manifold with zero Dirichlet boundary…

We obtain a sub-Riemannian version of the classical Gauss-Bonnet theorem. We consider subsurfaces of a three dimensional contact sub-Riemannian manifolds, and using a family of taming Riemannian metric, we obtain a pure sub-Riemannian…

The purpose of this article is to investigate Bach-flat critical metrics of the volume functional on a compact manifold $M$ with boundary $\partial M.$ Here, we prove that a Bach-flat critical metric of the volume functional on a simply…

For a compact connected Riemannian manifold with smooth boundary, by computing the full symbol of the elastic Dirichlet-to-Neumann map, we prove that the elastic Dirichlet-to-Neumann map can uniquely determine the partial derivatives of all…

We examine Hamilton-Jacobi equations driven by fully nonlinear degenerate elliptic operators in the presence of superlinear Hamiltonians. By exploring the Ishii-Jensen inequality, we prove that viscosity solutions are locally…

Under the assumption of the uniform local Sobolev inequality, it is proved that Riemannian metrics with an absolute Ricci curvature bound and a small Riemannian curvature integral bound can be smoothed to having a sectional curvature bound.…

The aim of this work is to deal with a discontinuous Hamilton-Jacobi equation in the whole euclidian N-dimensional space, associated to a possibly unbounded optimal control problem. Here, the discontinuities are located on a hyperplane and…

A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics. In the present paper, using the variational method for solving nonlinear boundary problems of…