相关论文: Global solutions to the thin obstacle problem with…

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation…

We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in [9],…

We consider singular perturbations of eigenvalue problems. We prove that to these problems correspond simple eigenvalues and we study their asymptotic behavior. As a result, we prove global bifurcation results for non uniformly and fully…

An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…

We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…

We establish the existence of positive solutions to a general class of overdetermined semilinear elliptic boundary problems on suitable bounded open sets $\Omega\subset\mathbb{R}^n$. Specifically, for $n\leq 4$ and under mild technical…

We develop a global bifurcation theory for two classes of nonlinear elastic materials. It is supposed that they are subjected to anti-plane shear deformation and occupy an infinite cylinder in the reference configuration. Curves of…

Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it…

This paper presents global optimal solutions to a nonconvex quadratic minimization problem over a sphere constraint. The problem is well-known as a trust region subproblem and has been studied extensively for decades. The main challenge is…

A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.

Global existence of mild solutions to the discrete collisional breakage equations is established for a broad class of collision kernels, without imposing any growth assumptions. In addition, classical solutions are constructed, and…

Obstacles to integrability in perturbed evolution equations are overcome by allowing higher-order terms in the expansion of the solution to depend explicitly on time and position. With a special expansion algorithm, obstacles vanish…

We consider anti-plane shear deformations of an incompressible elastic solid whose reference configuration is an infinite cylinder with a cross section that is unbounded in one direction. For a class of generalized neo-Hookean strain energy…

The global existence of weak solutions to the three space dimensional Prandtl equations is studied under some constraint on its structure. This is a continuation of our recent study on the local existence of classical solutions with the…

We prove optimal regularity and a detailed analysis of the free boundary of the solutions to the thin obstacle problem for nonparametric minimal surfaces with flat obstacles.

The constraints imposed on heterotic compactifications by global consistency and phenomenology seem to be very finely balanced. We show that weakening these constraints, as was proposed in some recent works, is likely to lead to frivolous…

In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Building on recent advances showing infinite sumsets can be found,…

Existence of solutions to an obstacle $p$-Laplacian problem exhibiting a singular, discontinuous reaction is proved. The reaction term may be discontinuous in a Lebesgue-negligible set. Moreover, solutions are shown to be locally…

The classical, linear-time solvable Feedback Edge Set problem is concerned with finding a minimum number of edges intersecting all cycles in a (static, unweighted) graph. We provide a first study of this problem in the setting of temporal…

Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly…