Related papers: Optimal Lipschitz criteria and local estimates for…
We investigate the quantitative unique continuation properties of solutions to second-order elliptic equations with lower-order terms. In particular, we establish quantitative forms of the strong unique continuation property for solutions…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…
In this paper, we extend the nontangential maximal function estimate obtained by C. Kenig, F. Lin and Z. Shen in \cite{KFS1} to the nonhomogeneous elliptic operators with rapidly oscillating periodic coefficients. The result relies on the…
This paper surveys recent analytical and numerical research on linear problems for the integral fractional Laplacian, fractional obstacle problems, and fractional minimal graphs. The emphasis is on the interplay between regularity,…
The main result of this paper is to prove that viscosity solutions to a parabolic free boundary problem with variable coefficients are Lipschitz continuous under the assumptions that the solution has a Lipschitz free boundary and satisfies…
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results obtained…
We establish a Lipschitz stability inequality for the problem of determining the nonlinear term in a quasilinear elliptic equation by boundary measurements. We give a proof based on a linearization procedure together with special solutions…
We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
We report on some recent existence and uniqueness results for elliptic equations subject to Dirichlet boundary condition and involving a singular nonlinearity. We take into account the following types of problems: (i) singular problems with…
We provide regularity results at the boundary for continuous viscosity solutions to nonconvex fully nonlinear uniformly elliptic equations and inequalities in Euclidian domains. We show that (i) any solution of two sided inequalities with…
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…
We consider regularised quadratic optimal transport with subquadratic polynomial or entropic regularisation. In both cases, we prove interior Lipschitz-estimates on a transport-like map and interior gradient Lipschitz-estimates on the…
This paper is concerned with the large-scale regularity in the homogenization of elliptic systems of elasticity with periodic high-contrast coefficients. We obtain the large-scale Lipschitz estimate that is uniform with respect to the…
We consider geodesics in both Riemannian and Lorentzian manifolds with metrics of low regularity. We discuss existence of extremal curves for continuous metrics and present several old and new examples that highlight their subtle…
We obtain $L^p(L^q)$ maximal regularity estimates for time dependent second order elliptic operators in divergence form with rough dependencies in the spatial variables.
The model problem of a plane angle for a second-order elliptic system subject to Dirichlet, mixed, and Neumann boundary conditions is analyzed. For each boundary condition, the existence of solutions of the form $r^\lambda v$ is reduced to…
We derive gradient and second order {\em a priori} estimates for solutions of the Neumann problem for a general class of fully nonlinear elliptic equations on compact Riemannian manifolds with boundary. These estimates yield regularity and…