Related papers: On global solutions of the obstacle problem

We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…

We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions,…

Optimization problems occurring in a wide variety of physical design problems, including but not limited to optical engineering, quantum control, structural engineering, involve minimization of a simple cost function of the state of the…

We prove an epiperimetric inequality for the thin obstacle problem, extending the pioneering results by Weiss on the classical obstacle problem (Invent. Math. 138 (1999), no. 1, 23-50). This inequality provides the means to study the rate…

In this paper, it is proved a very general well-posedness result for a class of constrained minimization problems.

We investigate the problem of deciding whether a system of linear equations, together with divisibility conditions on the variables, has a solution over holomorphy subrings of global fields. We obtain decidability results when we allow…

In this paper, we explore cooperative and competitive coupled obstacle systems, which, up to now, are new type obstacle systems and formed by coupling two equations belonging to classical obstacle problem. On one hand, applying the…

We obtain the global large solutions to the compressible Navier-Stokes equations in $\mathbb{R}^2$. The solution is large in the sense that there is no smallness assumption applied to one component of the initial incompressible velocity.

This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…

We propose a new approach to solving dynamic decision problems with rewards that are unbounded below. The approach involves transforming the Bellman equation in order to convert an unbounded problem into a bounded one. The major advantage…

Base on a conjecture, we prove that for any smooth separated stack of finite type over a number field, its descent obstruction equals its iterated descent obstruction. As a consequence, we show that for any algebraic stack over a number…

Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…

We prove that bounded solutions to an overdetermined fully nonlinear free boundary problem in the plane are one dimensional. Our proof relies on maximum principle techniques and convexity arguments.

We prove a result on the convex dependence of solutions of ordinary differential equations on an ordered finite-dimensional real vector space with respect to the initial data.

In this paper we provide an analytical framework for investigating the efficiency of a consensus-based model for tackling global optimization problems. This work justifies the optimization algorithm in the mean-field sense showing the…

We conjecture that if a system S \subseteq {x_i=1, x_i+x_j=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,...,n}} has only finitely many solutions in integers x_1,...,x_n, then each such solution (x_1,...,x_n) satisfies |x_1|,...,|x_n| \leq…

Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…

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,…

We consider a parabolic obstacle problem for Euler's elastic energy of graphs with fixed ends. We show global existence, well-posedness and subconvergence provided that the obstacle and the initial datum are suitably 'small'. For symmetric…

In this paper, we establish sufficient conditions for the existence of error bounds at infinity for lower semicontinuous inequality systems. We also show that the existence of an error bound at infinity of constraint systems plays an…