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We prove that $L^2$ weak solutions to hypoelliptic equations with bounded measurable coefficients are H\"older continuous. The proof relies on classical techniques developed by De Giorgi and Moser together with the averaging lemma and…

Analysis of PDEs · Mathematics 2015-06-22 Cyril Imbert , Clément Mouhot

This paper proposes a relaxed control regularization with general exploration rewards to design robust feedback controls for multi-dimensional continuous-time stochastic exit time problems. We establish that the regularized control problem…

Optimization and Control · Mathematics 2021-07-26 Christoph Reisinger , Yufei Zhang

We prove logarithmic conditional stability up to the final time for backward-parabolic operators whose coefficients are Log-Lipschitz continuous in $t$ and Lipschitz continuous in $x$. The result complements previous achievements of Del…

Analysis of PDEs · Mathematics 2022-08-30 Daniele Casagrande , Daniele Del Santo , Martino Prizzi

We study mappings with branching of a domain of Euclidean space. The H\"older and Lipschitz continuity are established for one class of spatial mappings whose characteristic satisfies the Dini type condition in a given domain. In addition,…

Complex Variables · Mathematics 2019-01-21 V. Ryazanov , R. Salimov , E. Sevost'yanov

In this paper, we study the mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with a parametric generalized equation involving the regular normal cone. Compared with the usual way of formulating…

Optimization and Control · Mathematics 2016-11-24 Helmut Gfrerer , Jane J. Ye

This paper investigates the relation between the boundary geometric properties and the boundary regularity of the solutions of elliptic equations. We prove by a new unified method the pointwise boundary H\"{o}lder regularity under proper…

Analysis of PDEs · Mathematics 2020-06-16 Yuanyuan Lian , Kai Zhang , Dongsheng Li , Guanghao Hong

The interest of the scientific community for the existence, uniqueness and stability of solutions to PDE's is testified by the numerous works available in the literature. In particular, in some recent publications on the subject an…

Analysis of PDEs · Mathematics 2019-02-22 Daniele Casagrande , Daniele Del Santo , Martino Prizzi

In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Francois Ebobisse , Marcello Ponsiglione

We start presenting an $L^{\infty}$-gradient bound for solutions to non-homogeneous $p$-Laplacean type systems and equations, via suitable non-linear potentials of the right hand side. Such a bound implies a Lorentz space characterization…

Analysis of PDEs · Mathematics 2015-05-14 Frank Duzaar , Giuseppe Mingione

We report on new techniques and results in the regularity theory of general non-uniformly elliptic variational integrals. By means of a new potential theoretic approach we reproduce, in the non-uniformly elliptic setting, the optimal…

Analysis of PDEs · Mathematics 2018-07-31 Lisa Beck , Giuseppe Mingione

In this paper, we consider a non-linear fourth-order evolution equation of Cahn-Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order…

Numerical Analysis · Mathematics 2022-03-07 Cedric Aaron Beschle , Balázs Kovács

This paper is dedicated to the stability analysis of the optimal solutions of a control problem associated with a semilinear elliptic equation. The linear differential operator of the equation is neither monotone nor coercive due to the…

Optimization and Control · Mathematics 2025-11-20 Eduardo Casas , Alberto Domínguez Corella , Nicolai Jork

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…

Optimization and Control · Mathematics 2025-03-04 Ion Necoara , Daniela Lupu

We investigate positive definiteness, Hurwitz stability and Schur stability of parametric interval matrices. We give a verifiable sufficient condition for positive definiteness of parametric interval matrices with non-linear dependencies.…

Numerical Analysis · Mathematics 2017-09-05 Iwona Skalna

Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…

Probability · Mathematics 2024-09-30 István Gyöngy , Nicolai V. Krylov

We generalize the reduction mechanism for linear programming problems and semidefinite programming problems from [arXiv:1410.8816] in two ways 1) relaxing the requirement of affineness and 2) extending to fractional optimization problems.…

Computational Complexity · Computer Science 2018-10-23 Gábor Braun , Sebastian Pokutta , Aurko Roy

The present paper is focused on the computation of the Lipschitz upper semicontinuity modulus of the feasible set mapping in the context of fully perturbed linear inequality systems; i.e., where all coefficients are allowed to be perturbed.…

Optimization and Control · Mathematics 2025-05-06 Jesús Camacho , María Josefa Cánovas , Helmut Gfrerer , Juan Parra

A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are…

Mathematical Physics · Physics 2015-03-03 Oskar Sultanov

This paper is devoted to the study of tilt stability of local minimizers for classical nonlinear programs with equality and inequality constraints in finite dimensions described by twice continuously differentiable functions. The importance…

Optimization and Control · Mathematics 2016-11-24 Helmut Gfrerer , Boris S. Mordukhovich

This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…

Functional Analysis · Mathematics 2025-12-16 M. H. M. Rashid