Related papers: A Regularity Theory for Stationary Two-valued Harm…
In a Hilbert space setting, we study the stability properties of the regularized continuous Newton method with two potentials, which aims at solving inclusions governed by structured monotone operators. The Levenberg-Marquardt…
This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions. It is shown…
The theory of boundary regularity for $p$-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The barrier classification of regular…
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range amongst those with unbalanced…
In this paper, we study the regularity of several notions of Lipschitz solutions to the minimal surface system with an emphasis on partial regularity results. These include stationary solutions, integral weak solutions, and viscosity…
The aim of this article is to present a concise proof for the interior H\"{o}lder continuity of two-dimensional stationary Q-valued maps. The proof employs a blow-up argument based on the monotonicity formula for the frequency function,…
Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…
The regularity theory of the Campanato space $\mathcal{L}^{(q,\lambda)}_k(\Omega)$ has found many applications within the regularity theory of solutions to various geometric variational problems. Here we extend this theory from…
We obtain Lipschitz regularity results for a fairly general class of nonlinear first-order PDEs. These equations arise from the inner variation of certain energy integrals. Even in the simplest model case of the Dirichlet energy the…
We present a general blow-up technique to obtain local regularity estimates for solutions, and their derivatives, of second order elliptic equations in divergence form in H\"older spaces with variable exponent. The procedure allows to…
We study the regularity of the interface between the disjoint supports of a pair of nonnegative subharmonic functions. The portion of the interface where the Alt-Caffarelli-Friedman (ACF) monotonicity formula is asymptotically positive…
The central theme in this paper is the Hopf-Laplace equation, which represents stationary solutions with respect to the inner variation of the Dirichlet integral. Among such solutions are harmonic maps. Nevertheless, minimization of the…
In this article, we study the regularity of minimizing and stationary $p$-harmonic maps between Riemannian manifolds. The aim is obtaining Minkowski-type volume estimates on the singular set $S(f)=\{x \ \ s.t. \ \ f \text{ is not continuous…
To minimize or upper-bound the value of a function "robustly", we might instead minimize or upper-bound the "epsilon-robust regularization", defined as the map from a point to the maximum value of the function within an epsilon-radius. This…
This work extends monotonicity-based methods in inverse problems to the case of the Helmholtz (or stationary Schr\"odinger) equation $(\Delta + k^2 q) u = 0$ in a bounded domain for fixed non-resonance frequency $k>0$ and real-valued…
We construct deterministic solutions to the Helmholtz equation in $\mathbb{R}^m$ which behave accordingly to the Random Wave Model. We then find the number of their nodal domains, their nodal volume and the topologies and nesting trees of…
We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being…
In this paper we consider Lipschitz graphs of functions which are stationary points of strictly polyconvex energies. Such graphs can be thought as integral currents, resp. varifolds, which are stationary for some elliptic integrands. The…
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…
In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is…