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In this paper, we investigate boundary estimates for the Dirichlet problem for a class of fully nonlinear elliptic equations with general boundary conditions, including nonzero boundary conditions. Given specific structural conditions on…
F.-H. Lin studied minimal graphs of the Dirichlet problem in the hyperbolic space and proved that any such minimal graph has the same global regularity as the boundary if the dimension of the minimal graph is even and that there is an…
Comparing Neumann and Dirichlet eigenvalues of the Laplacian on a bounded domain $\Omega\subseteq\Rbb^n$ is a topic that goes back at least to the work of P\'olya \cite{polya}. We study the effect of the isoperimetric ratio of $\Omega$ on…
We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the…
We exploit the existence and nonlinear stability of boundary spike/layer solutions of the Keller-Segel system with logarithmic singular sensitivity in the half space, where the physical zero-flux and Dirichlet boundary conditions are…
In this paper, we consider the transmission eigenvalue problem associated with a general conductive transmission condition and study the geometric structures of the transmission eigenfunctions. We prove that under a mild regularity…
We establish several results related to existence, nonexistence or bifurcation of positive solutions for a Dirichlet boundary value problem with in a smooth bounded domain. The main feature of this paper consists in the presence of a…
We consider the semilinear heat equation with a superlinear nonlinearity and we study the properties of threshold or subthreshold solutions, lying on or below the boundary between blow-up and global existence, respectively. For the…
In this paper, we study the regularity of asymptotically hyperbolic metrics with Einstein condition near boundary and Weyl curvature smooth enough in arbitrary dimension. Following Michael Anderson's method, we show that $C^{m,\alpha}$…
Oleinik's \emph{no back-flow} condition ensures the existence and uniqueness of solutions for the Prandtl equations in a rectangular domain $R\subset \mathbb{R}^2$. It also allowed us to find a limit formula for Dorodnitzyn's stationary…
For closed connected Riemannian spin manifolds an upper estimate of the smallest eigenvalue of the Dirac operator in terms of the hyperspherical radius is proved. When combined with known lower Dirac eigenvalue estimates, this has a number…
Given the wave equation on a compact Riemannian manifold with boundary, we derive an explicit reconstruction procedure to represent the frequency-domain Neumann-to-Dirichlet map in terms of the time-domain Neumann-to-Dirichlet map at any…
Boundary value problems for second-order elliptic equations in divergence form, whose nonlinearity is governed by a convex function of non-necessarily power type, are considered. The global boundedness of their solutions is established…
We prove lower bound for the first closed or Neumann nonzero eigenvalue of the Laplacian on a compact quaternion-K\"ahler manifold in terms of dimension, diameter, and scalar curvature lower bound. It is derived as large time implication of…
Despite the physical importance, there are limited mathematical theories for the compressible Navier-Stokes equations with strong boundary layers. This is mainly due to the absence of a stream function structure, unlike the extensively…
We provide a manifestly topological classification scheme for generalised Weyl semimetals, in any spatial dimension and with arbitrary Weyl surfaces which may be non-trivially linked. The classification naturally incorporates that of Chern…
Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general…
This work addresses the Galerkin isogeometric discretization of the one-dimensional Laplace eigenvalue problem subject to homogeneous Dirichlet boundary conditions on a bounded interval. We employ GLT theory to analyze the behavior of the…
One of the main statistical features of near-neutral atmospheric boundary layer (ABL) turbulence is the positive vertical velocity skewness $Sk_w$ above the roughness sublayer or the buffer region in smooth-walls. The $Sk_w$ variations are…
A scaling relation for the high frequency regime of streamwise energy spectra (in frequency domain) in the near-wall region is proposed. This is based on the dimensional analysis approach of \cite{perry1977} and \cite{Zamalloa2014} together…