Related papers: Irregular Time Dependent Obstacles
This paper deals with the Lipschitz regularity of minimizers for a class of variational obstacle problems with possible occurance of the Lavrentiev phenomenon. In order to overcome this problem, the availment of the notions of relaxed…
We consider elliptic variational inequalities generated by obstacle type problems with thin obstacles. For this class of problems, we deduce estimates of the distance (measured in terms of the natural energy norm) between the exact solution…
We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle…
We prove an existence and uniqueness result for the obstacle problem of quasilinear parabolic stochastic PDEs. The method is based on the probabilistic interpretation of the solution by using the backward doubly stochastic differential…
In this paper, we propose a new framework for solving a general dynamic optimal stopping problem without time consistency. A sophisticated solution is proposed and is well-defined for any time setting with general flows of objectives. A…
We study quasilinear evolutionary partial integro-differential equations of second order which include time fractional $p$-Laplace equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration…
Let us consider the autonomous obstacle problem \begin{equation*} \min_v \int_\Omega F(Dv(x)) \, dx \end{equation*} on a specific class of admissible functions, where we suppose the Lagrangian satisfies proper hypotheses of convexity and…
We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.
We study the double-obstacle problem for the p-Laplace operator, p 2 [2;1). We prove that for Lipschitz boundary data and Lipschitz obstacles, viscosity solutions are unique and coincide with variational solutions. They are also uniform…
In this article we study the existence and uniqueness of solutions of stochastic continuity equation with irregular coefficients.
We establish the higher differentiability of solutions to a class of obstacle problems for integral functionals where the convex integrand f satisfies p-growth conditions with respect to the gradient variable. We derive that the higher…
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…
We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like penalty on the variational problem. The reformulation is an…
We discuss the unstable character of the solutions of the Lorentz-Dirac equation and stress the need of methods like order reduction to derive a physically acceptable equation of motion. The discussion is illustrated with the paradigmatic…
Evolutionary algorithms have been frequently applied to constrained continuous optimisation problems. We carry out feature based comparisons of different types of evolutionary algorithms such as evolution strategies, differential evolution…
We consider the periodic Manhattan lattice with alternating orientations going north-south and east-west. Place obstructions on vertices independently with probability $0<p<1$. A particle is moving on the edges with unit speed following the…
We consider an evolution equation involving the fractional powers, of order $s \in (0,1)$, of a symmetric and uniformly elliptic second order operator and Caputo fractional time derivative of order $\gamma \in (1,2]$. Since it has been…
We study some Dirichlet problem for a $p$--Laplacian type operator in the setting of Orlicz--Zygmund space $L^q\log^{-\alpha}L(\Omega,\mathbb R^N)$, $q >1$ and $\alpha>0$. More precisely, our aim is to establish which assuptions on the…
In this paper, we study the large deviation principle (LDP) for obstacle problems governed by a T-monotone operator and small multiplicative stochastic reaction. Our approach relies on a combination of new sufficient condition to prove LDP…
We introduce a novel monotone discretization method for addressing obstacle problems involving the integral fractional Laplacian with homogeneous Dirichlet boundary conditions over bounded Lipschitz domains. This problem is prevalent in…