Related papers: Asymptotically quasiconvex functionals with genera…

In [2] we characterized in terms of a quadratic growth condition various metric regularity properties of the subdifferential of a lower semicontinuous convex function acting in a Hilbert space. Motivated by some recent results in [16] where…

This paper introduces and investigates a regularity condition in the asymptotic sense for optimization problems whose objective functions are polynomial. Under this regularity condition, the normalization argument in asymptotic analysis…

The goal of this note is to prove that every real-valued Lipschitz function on a Banach space can be pointwise approximated on a given $\sigma$-compact set by smooth cylindrical functions whose asymptotic Lipschitz constants are controlled.…

Let $(M,g)$ be a smooth connected Riemannian manifold. We show an improvement of flatness theorem for hypersurfaces of $M$ of bounded nonlocal mean curvature in the viscosity sense. It implies local $ C^{1,\alpha}$ regularity of these…

In this paper we introduce a notion of almost minimizers for certain variational problems governed by the fractional Laplacian, with the help of the Caffarelli-Silvestre extension. In particular, we study almost fractional harmonic…

We study Lusin-measurable functions with values in locally convex spaces. In particular, the behavior of pointwise limits of sequences of Lusin-measurable functions and exhibit pathological phenomena arising in the nonmetrizable setting.…

Let $(g^{\alpha\beta}(x))$ and $(h_{ij}(u))$ be uniformly elliptic symmetric matrices, and assume that $h_{ij}(u)$ and $p(x) \, (\, \geq 2)$ are sufficiently smooth. We prove partial regularity of minimizers for the functional [ {\mathcal…

We study various regularity properties of minimizers of the $\Phi$--perimeter, where $\Phi$ is a norm. Under suitable assumptions on $\Phi$ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is…

We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which…

The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid…

As one myth of polynomial interpolation and quadrature, Trefethen [30] revealed that the Chebyshev interpolation of $|x-a|$ (with $|a|<1 $) at the Clenshaw-Curtis points exhibited a much smaller error than the best polynomial approximation…

We study the qualitative properties of functions belonging to the corresponding De Giorgi classes \begin{equation*} \int\limits_{B_{r(1-\sigma)}(x_{0})}\,\varPhi(x, |\nabla(u-k)_{\pm}|)\,dx \leqslant…

For a class of symplectic manifolds, we introduce a functional which assigns a real number to any pair of continuous functions on the manifold. This functional has a number of interesting properties. On the one hand, it is Lipschitz with…

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…

We deal with homogeneous Dirichlet and Neumann boundary-value problems for anisotropic elliptic operators of p-Laplace type. They emerge as Euler-Lagrange equations of integral functionals of the Calculus of Variations built upon possibly…

Given a family of locally Lipschitz vector fields $X(x)=(X_1(x),\dots,X_m(x))$ on $\mathbb{R}^n$, $m\leq n$, we study integral functionals depending on $X$. Using the results in \cite{MPSC1}, we study the convergence of minima, minimizers…

We establish interior regularity and optimal growth estimates for sign-changing minimizers of the $p-$singular or $p-$degenerate quasilinear Alt--Phillips functional throughout the full range of $1<p<\infty$ and of the nonlinearity power…

We study minimizers of non-autonomous functionals \begin{align*} \inf_u \int_\Omega \varphi(x,|\nabla u|) \, dx \end{align*} when $\varphi$ has generalized Orlicz growth. We consider the case where the upper growth rate of $\varphi$ is…

We give a direct harmonic approximation lemma for local minima of quasiconvex multiple integrals that entails their $\mathrm{C}^{1,\alpha}$ or $\mathrm{C}^{\infty}$-partial regularity. Different from previous contributions, the method is…

We study maximal regularity with respect to continuous functions for strongly continuous semigroups on locally convex spaces as well as its relation to the notion of admissible operators. This extends several results for classical strongly…