Related papers: Remarks on Nehari's problem, matrix $A_2$ conditio…
Fast and accurate resolution of electromagnetic problems via the \ac{BEM} is oftentimes challenged by conditioning issues occurring in three distinct regimes: (i) when the frequency decreases and the discretization density remains constant,…
We consider the fourth order problem $\Delta^{2}u=\lambda f(u)$ on a general bounded domain $\Omega$ in $R^{n}$ with the Navier boundary condition $u=\Delta u=0$ on $\partial \Omega$. Here, $\lambda$ is a positive parameter and $…
In this paper we initiate the investigation of free boundary minimization problems ruled by general singular operators with $A_2$ weights. We show existence and boundedness of minimizers. The key novelty is a sharp $C^{1+\gamma}$ regularity…
We consider the space $A(\mathbb{T}^d)$ of absolutely convergent Fourier series on the torus $\mathbb{T}^d$. The norm on $A(\mathbb{T}^d)$ is naturally defined by $\|f\|_{A}=\|\widehat{f}\|_{l^1}$, where $\widehat{f}$ is the Fourier…
In this manuscript, we consider a structural acoustic model consisting of a wave equation defined in a bounded domain $\Omega \subset \mathbb{R}^3$, strongly coupled with a Berger plate equation acting on the flat portion of the boundary of…
We consider the problem of satisfaction of boundary conditions when the generalized stress vector is given on the surfaces for elastic plates and shells. This problem was open also both for refined theories in the wide sense and…
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…
In this paper, we study the existence of solutions to a type of super-Liouville equation on the compact Riemannian surface $M$ with boundary and with its Euler characteristic $\chi(M)<0$. The boundary condition couples a Neumann condition…
We formulate and study an elliptic transmission-like problem combining local and nonlocal elements. Let $\mathbb{R}^{n}$ be separated into two components by a smooth hypersurface $\Gamma$. On one side of $\Gamma$, a function satisfies a…
In the present paper we establish the solvability of the Regularity boundary value problem in domains with (flat and Lipschitz) lower dimensional boundaries for operators whose coefficients exhibit small oscillations analogous to the…
We establish the H\"older continuity of bounded nonnegative weak solutions to \begin{align*} \big(\Phi^{-1}(w)\big)_t=\Delta w+\nabla\cdot\big(a(x,t)\Phi^{-1}(w)\big)+b\big(x,t,\Phi^{-1}(w)\big), \end{align*} with convex $\Phi\in…
Modern data analysis depends increasingly on estimating models via flexible high-dimensional or nonparametric machine learning methods, where the identification of structural parameters is often challenging and untestable. In linear…
We consider the problem of minimizing the Lagrangian $\int [F(\nabla u)+f\,u]$ among functions on $\Omega\subset\mathbb{R}^N$ with given boundary datum $\varphi$. We prove Lipschitz regularity up to the boundary for solutions of this…
We reinterpret various properties of Noetherian local rings via the existence of some $n$-ary numerical function satisfying certain uniform bounds. We provide such characterizations for seminormality, weak normality, generalized…
In this short paper we show that March's criterion for the existence of a bounded non constant harmonic function on a weak model is also a necessary and sufficient condition for the solvability of the Dirichlet problem at infinity on a…
Let $(X,\mathcal{A}, \mu)$ be a probability measure space and let $T_i,$ $1\leq i\leq H,$ be invertible bi measurable measure preserving transformations on this measure space. We give a sufficient condition for the product of $H$ bounded…
We investigate the presence of rotating wave solutions of the nonlinear wave equation $\partial_t^2 v - \Delta v +m v = |v|^{p-2} v$ in $\mathbb{R} \times \mathbf{B}$, where $\mathbf{B} \subset \mathbb{R}^N$ is the unit ball, complemented…
Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. We initiate the corresponding study of higher critical points by considering a superlinear free boundary problem…
The focusing NLS equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, considered the main physical mechanism for the appearance of rogue (anomalous)…
It is establish regularity results for weak solutions of quasilinear elliptic problems driven by the well known $\Phi$-Laplacian operator given by \begin{equation*} \left\{\ \begin{array}{cl} \displaystyle-\Delta_\Phi u= g(x,u), &…