Related papers: Local inverse estimates for non-local boundary int…

We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on…

The squared Laplace operator acting on symmetric rank-two tensor fields is studied on a (flat) Riemannian manifold with smooth boundary. Symmetry of this fourth-order elliptic operator is obtained provided that such tensor fields and their…

Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust…

This is a survey of recent results on zeta- and eta-function poles and values for realizations of Laplace- and Dirac-type operators defined by pseudodifferential projection boundary conditions (including the Atiyah-Patodi-Singer operator…

We prove several off-diagonal and pointwise estimates for singular integral operators that extend compactly on $L^{p}(\mathbb R^{n})$.

We consider an inverse problem for the double layer potential which can be formulated, somewhat loosely, as follows. For which smoothly bounded domains D in Euclidian space does the operator J, which maps a function on the boundary to the…

We study second-order elliptic partial differential operators acting on sections of vector bundles over a compact manifold with boundary with a non-scalar positive definite leading symbol. Such operators, called non-Laplace type operators,…

Let $\Omega$ be a piecewise-smooth, bounded convex domain in $\R^2$ and consider $L^2$-normalized Neumann eigenfunctions $\phi_{\lambda}$ with eigenvalue $\lambda^2$. Our main result is a small-scale {\em non-concentration} estimate: We…

In this paper we study the inverse boundary value problem of determining the potential in the Schr\"{o}dinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that,…

Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…

For bounded domains $\Omega$ with Lipschitz boundary $\Gamma$, we investigate boundary value problems for elliptic operators with variable coefficients of fourth order subject to Wentzell (or dynamic) boundary conditions. Using form…

Let $\Omega \subset \mathbb{R}^d$ be a bounded open connected set with Lipschitz boundary. Let $A^N$ and $A^D$ be the Neumann Stokes operator and Dirichlet Stokes operator on $\Omega$, respectively. Further let $\lambda_1^N \leq \lambda_2^N…

We consider the spectrum of the Laplace operator on 3D rod structures, with a small cross section depending on a small parameter $\varepsilon$. The boundary conditions are of Dirichlet type on the basis of this structure and Neumann on the…

Let $\Omega$ be an $n$-dimensional compact Riemannian manifold $(n \geq 3)$ with $C^\infty$ boundary, and consider $L^2$-normalized eigenfunctions $ - \Delta \phi_{\lambda} = \lambda^2 \phi_\lambda$ with Dirichlet or Neumann boundary…

We prove a boundary Harnack inequality for nonlocal elliptic operators $L$ in non-divergence form with bounded measurable coefficients. Namely, our main result establishes that if $Lu_1=Lu_2=0$ in $\Omega\cap B_1$, $u_1=u_2=0$ in…

We establish sharp higher-order H\"older regularity estimates up to the boundary for solutions to equations of the form $\partial_t u-Lu=f(t,x)$ in $I\times\Omega$ where $I\subset\mathbb{R}$, $\Omega\subset\mathbb{R}^n$ and $f$ is H\"older…

This paper deals with the homogenization of a mixed boundary value problem for the Laplace operator in a domain with locally periodic oscillating boundary. The Neumann condition is prescribed on the oscillating part of the boundary, and the…

In this paper, the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian measure spaces associated with the local weights. More precisely, the authors first obtain…

In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth…

We propose a method of obtaining a posteriori estimates which does not use the duality theory and which applies to variational inequalities with monotone operators, without assuming the potentiality of operators. The effectiveness of the…