Related papers: Wiener-type tests from a two-sided Gaussian bound
This paper considers the Helmholtz problem in the exterior of a ball with Dirichlet boundary conditions and radiation conditions imposed at infinity. The differential Helmholtz operator depends on the complex wavenumber with non-negative…
We analyse the structure of semiclassical and microlocal Wigner measures for solutions to the linear Schr\"{o}dinger equation on the disk, with Dirichlet boundary conditions. Our approach links the propagation of singularities beyond…
We provide a new version of the Wiener-Ikehara theorem where one deduces bounds $$ 0< \liminf_{x\to\infty} \frac{S(x)}{e^{x}}\leq \limsup_{x\to\infty} \frac{S(x)}{e^{x}} <\infty $$ for (in particular) a non-decreasing function $S$ from a…
We prove sharp boundary H{\"o}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini}}$-property. This result is new even for the fractional…
In this short note we outline a simple probabilistic proof of the Gauss-Bonnet formula for compact Riemannian manifolds with boundary, which adapts to this setting an argument due to Hsu \cite{Hs1,Hs2} in the closed case. The new technical…
We survey some recent regularity results for fractional p-Laplacian elliptic equations, especially focusing on pure and weighted boundary H\"older continuity of the solutions of related Dirichlet problems. Then, we present some applications…
We obtain sufficient conditions expressed in terms of Wiener type tests involving Hausdorff or Bessel capacities for the existence of large solutions to equations (1) $-\Gd_pu+e^{\lambda u}+\beta=0$ or (2) $-\Gd_pu+\lambda…
In this paper we relax the current regularity theory for the eikonal equation by using the recent theory of { set-valued} iterated Lie brackets. We give sufficient conditions for small time local attainability of general, symmetric,…
We initiate the study of noncharacteristic boundary layers in hyperbolic-parabolic problems with Neumann boundary conditions. More generally, we study boundary layers with mixed Dirichlet--Neumann boundary conditions where the number of…
In this paper, we study the global regularity for regular Monge-Amp\`ere type equations associated with semilinear Neumann boundary conditions. By establishing a priori estimates for second order derivatives, the classical solvability of…
We prove the existence of solution in a class H^2(\Omega) x H^1(\Omega) to steady compressible Oseen system with slip boundary conditions in a two dimensional, convex domain with the boundary of class H^{5/2}. The method is to regularize a…
In the first part of this work, we analyzed a Dirichlet boundary control problem for an elliptic convection diffusion PDE and proposed a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For the case of a 2D…
We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well-posedness of the inversion in terms of the boundary conditions. We…
We investigated an hybridizable discontinuous Galerkin (HDG) method for a convection diffusion Dirichlet boundary control problem in our earlier work [SIAM J. Numer. Anal. 56 (2018) 2262-2287] and obtained an optimal convergence rate for…
We study the boundary regularity properties and derive a priori pointwise supremum estimates of weak solutions and their derivatives in terms of suitable weighted $L^2$-norms for a class of degenerate parabolic equations that satisfy…
Let $\Omega$ be a bounded, pseudoconvex domain of $\mathbb C^n$ satisfying the "$f$-Property". The $f$-Property is a consequence of the geometric "type" of the boundary; it holds for all pseudoconvex domains of finite type but may also…
We study a Dirichlet boundary value problem associated to an anisotropic differential operator on a smooth bounded of $\Bbb R^N$. Our main result establishes the existence of at least two different non-negative solutions, provided a certain…
We investigate the regularity issue for the diffuse reflection boundary problem to the stationary linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or cutoff Maxwellian molecular gases in a strictly convex…
Let $\Omega \subset \mathbb C^n$ be a bounded strictly $m$-pseudoconvex domain ($1\leq m\leq n$) and $\mu$ a positive Borel measure on $\Omega$. We study the Dirichlet problem for the complex Hessian equation $(dd^c u)^m \wedge \beta^{n -…
We consider the $2m$-th order elliptic boundary value problem $Lu=f(x,u)$ on a bounded smooth domain $\Omega$ in $R^N$ with Dirichlet boundary conditions. The operator $L$ is a uniformly elliptic operator of order $2m$. We assume that for…