Related papers: Explicit bounds for Lipschitz constant of solution…
In this article, we provide sufficient conditions under which the controlled vector fields solution of optimal control problems formulated on continuity equations are Lipschitz regular in space. Our approach involves a novel combination of…
A class of parametric optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is investigated. The perturbations appear in the objective functional, the state equation and in mixed pointwise…
The existence and uniqueness of a solution to a generalized Blasius equation with asymptotic boundary conditions are proved. A new numerical approximation method is proposed.
The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the…
In this paper, we trace the development of the theory of the calculus of variations. From its roots in the work of Greek thinkers and continuing through to the Renaissance, we see that advances in physics serve as a catalyst for…
Lipschitz constants are connected to many properties of neural networks, such as robustness, fairness, and generalization. Existing methods for computing Lipschitz constants either produce relatively loose upper bounds or are limited to…
Lipschitz learning is a graph-based semi-supervised learning method where one extends labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a weighted graph. In this work we prove uniform convergence…
In the article the necessary and sufficient conditions for a representation of Lipschitz function of two variables as a difference of two convex functions are formulated. An algorithm of this representation is given. The outcome of this…
In this work, we investigate the convergence of numerical approximations to coercivity constants of variational problems. These constants are essential components of rigorous error bounds for reduced-order modeling; extension of these…
The theory of imprecise Markov chains has achieved significant progress in recent years. Its applicability, however, is still very much limited, due in large part to the lack of efficient computational methods for calculating…
We consider the Dirichlet problem for elliptic systems with periodically distributed inclusions whose conduction parameter exhibits a significant contrast compared to the background media. We develop a unified method to quantify the…
This note is devoted to continuity results of the time derivative of the solution to the one-dimensional parabolic obstacle problem with variable coefficients. It applies to the smooth fit principle in numerical analysis and in financial…
We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map as the data. We consider piecewise constant wavespeeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
Variational problems under uniform quasiconvex constraints on the gradient are studied. In particular, existence of solutions to such problems is proved as well as existence of lagrange multipliers associated to the uniform constraint. They…
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 deal with probabilistic numerical solutions for linear elliptic equations with Neumann boundary conditions in a Lipschitz domain, by using a probabilistic numerical scheme introduced by Milstein and Tretyakov based on new numerical layer…
We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…
We consider inverse problems for the first and half order time fractional equation. We establish the stability estimates of Lipschitz type in inverse source and inverse coefficient problems by means of the Carleman estimates.
In this paper, we derive a local Carleman estimate for the complex second order elliptic operator with Lipschitz coefficients having jump discontinuities. Combing the result in [BL] and the arguments in [DcFLVW], we present an elementary…