Related papers: Infinity-Laplacians on Scalar- and Vector-Valued F…

This paper consists of two parts. In the first part, which is of more abstract nature, the notion of quasi boundary triples and associated Weyl functions is developed further in such a way that it can be applied to elliptic boundary value…

We prove an asymptotic formula for the determinant of the bundle Laplacian on discrete $d$-dimensional tori as the number of vertices tends to infinity. This determinant has a combinatorial interpretation in terms of cycle-rooted spanning…

In this report, we consider extended real-valued functions on some real vector space. Gerstewitz functionals are used to construct all translative functions. We derive formulas for translative functions which are lower semicontinuous,…

We consider an arbitrary selfadjoint operator on a separable Hilbert space. To this operator we construct an expansion in generalized eigenfunctions in which the original Hilbert space is decomposed as a direct integral of Hilbert spaces…

We study the uniqueness of self-adjoint and Markovian extensions of the Laplacian on weighted graphs. We first show that, for locally finite graphs and a certain family of metrics, completeness of the graph implies uniqueness of these…

This work advances knowledge of the threshold of prox-boundedness of a function; an important concern in the use of proximal point optimization algorithms and in determining the existence of the Moreau envelope of the function. In finite…

Hypergraphs extend traditional graphs by enabling the representation of N-ary relationships through higher-order edges. Akin to a common approach of deriving graph Laplacians, we define function spaces and corresponding symmetric products…

A classification of upper semicontinuous, translation and dually epi-translation invariant valuations is established on the space of convex Lipschitz function on $\mathbb{R}$ with compact domain.

We derive quantitative bounds for eigenvalues of complex perturbations of the indefinite Laplacian on the real line. Our results substantially improve existing results even for real-valued potentials. For $L^1$-potentials, we obtain optimal…

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…

This work provides the foundation for the finite element analysis of an elliptic problem which is the rotational analogue of the $p$-Laplacian and which appears as a model of the magnetic induction in a high-temperature superconductor…

We consider overdetermined boundary value problems for the $\infty$-Laplacian in a domain $\Omega$ of $\R^n$ and discuss what kind of implications on the geometry of $\Omega$ the existence of a solution may have. The classical…

Let $Q$ be a first-order differential operator on a compact, smooth oriented Riemannian manifold with smooth boundary. Then, Friedrichs' extension lemma states that the minimal closed extension $Q_{min}$ (the closure of the graph) and the…

We develop a new approach to the invertibility of the layer potentials on $L^p$ associated with elliptic equations and systems in Lipschitz domains. As a consequence, for $n\ge 4$ and $(2(n-1)/(n+1))-\epsilon<p<2$, we obtain the solvability…

The scalar G{\"u}nter derivatives of a function defined on the boundary of a three-dimensional domain are expressed as components (or their opposites) of the tangential vector rotational of this function in the canonical orthonormal basis…

This paper is concerned with the study of a nonlinear problems involving the fractional p(x)-Laplacian operator. By means of the Berkovits degree theory, we prove the existence of nontrivial weak solutions for this problem. The appropriate…

For $\Pi \subset \mathbb{R}^2$ a connected, open, bounded set whose boundary is a finite union of disjoint polygons whose vertices have integer coordinates, the logarithm of the discrete Laplacian on $L\Pi \cap \mathbb{Z}^2$ with Dirichlet…

The solutions of boundary value problems for the Laplacian and the bilaplacian exhibit very different qualitative behaviors. Particularly, the failure of general maximum principles for the bilaplacian implies that solutions of higher-order…

We prove fine higher regularity results of Calder\'on-Zygmund-type for equations involving nonlocal operators modelled on the fractional $p$-Laplacian with possibly discontinuous coefficients of VMO-type. We accomplish this by establishing…

We develop some properties of the $p-$Neumann derivative for the fractional $p-$Laplacian in bounded domains with general $p>1$. In particular, we prove the existence of a diverging sequence of eigenvalues and we introduce the evolution…