In this paper, we introduced a new way to analyze the shape using a new Fourier based descriptor, which is the smoothed derivative of the phase of the Fourier descriptors. It is extracted from the complex boundary of the shape, and is called the smoothed group delay (SGD). The usage of SGD on the Fourier phase descriptors, allows a compact representation of the shape boundaries which is robust ...

We study the existence and uniqueness of solutions to the static vacuum Einstein equations in bounded domains, satisfying the Bartnik boundary conditions of prescribed metric and mean curvature on the boundary.

In the present paper, we study uniform approximation of bounded functions on an open subset of the Euclidean space d by means of harmonic functions arising as solutions of the classical or generalized Dirichlet problem. As a consequence of results obtained we establish a harmonic analogue of Sarason’s H + C – theorem; see e. g. [5]. We shall consider an arbitrary bounded open subset of , d ≥ 2....

We consider the stabilization of the wave equation with space variable coefficients in a bounded region with a smooth boundary, subject to Dirichlet boundary conditions on one part of the boundary and linear or nonlinear dissipative boundary conditions of memory type on the remainder part of the boundary. Our stabilization results are mainly based on the use of differential geometry arguments, ...

We prove optimal boundary regularity for bounded positive weak solutions of fast diffusion equations in smooth domains. This solves a problem raised by Berryman and Holland 1980 these the subcritical critical regimes. Our proof priori estimates uses geometric type structure equations, where an important ingredient is evolution equation curvature-like quantity.

Abstract This paper studies the structure and stability of boundaries in noncollapsed $${{\,\mathrm{RCD}\,}}(K,N)$$ RCD ( K , N ) spaces, that is, metric-measure spaces $$(X,{\mathsf {d}}...

On a bounded strictly pseudoconvex domain in $\Bbb{C}^n$, $n>1$, the smoothness of Cheng-Yau solution to Fefferman's complex Monge-Ampere equation up boundary is obstructed by local curvature invariant boundary. For domains $\Bbb{C}^2$ which are diffeomorphic ball, we motivate and consider problem determining whether global vanishing this obstruction implies biholomorphic equivalence unit ball....

A combined analytical, numerical, and experimental study of the traveling-wave wall mode in rotating Rayleigh-Bénard convection is presented. No-slip top and bottom boundary conditions are used for the numerical computation of the linear stability, and the coefficients of the linear complex Ginzburg-Landau equation are then computed for various rotation rates. Numerical results for the no-slip ...