In this paper, we investigate optimal control problems for Allen–Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace– Beltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribe...

In this paper we discuss a special class of Beltrami coefficients whose associated quasiconformal mapping is bilipschitz. A particular example are those of the form f(z)χΩ(z), where Ω is a bounded domain with boundary of class C1+ε and f a function in Lip(ε,Ω) satisfying ‖f‖∞ < 1. An important point is that there is no restriction whatsoever on the Lip(ε,Ω) norm of f besides the requirement on ...

We address the problem of texture segmentation in the context of the Gabor feature space of images. Gabor filters which are tuned to different orientations, scales and frequencies are applied to textured images to create the Gabor feature space. We regard the scale, orientation and frequency for which maximum response of the Gabor filters was obtained. A two-dimensional Riemannian manifold of l...

The cooperation of nonlinearity ~producing collapsed characteristics! and dispersion ~unfolding singularities! underlies a robust mechanism that imparts two distinct scales (L measuring the system size, and d i typically of the order of the ion skin depth! to the double Beltrami states of a two-fluid plasma. It is shown that the conventional single-fluid model @magnetohydrodynamic ~MHD!# seemin...

We define a discrete Laplace-Beltrami operator for simplicial surfaces (Definition 16). It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called “cotan formula”) except that it is based on the intrinsic Delaunay triangulation of the simplicial surface. This leads to new ...

In this paper we continue the study of functional calculus for the Laplace{ Beltrami operator on symmetric spaces of the noncompact type begun in 3]; this paper is dedicated to a study of the Poisson semigroup, which we deene shortly. Let G and K be a connected noncompact semisimple Lie group with nite center and a maximal compact subgroup thereof, and consider the symmetric space G=K; also den...

A numerical method for quasiconformal mapping of doubly connected domains onto annuli is presented. The ratio R of the radii of the annulus is not known a priori and is determined as part of the solution procedure. The numerical method presented in this paper requires solving iteratively a sequence of inhomogeneous Beltrami equations, each for a diierent R. R is updated using a procedure based ...

Abstract Exact flows of an incompressible fluid satisfying the Beltrami equation inside a spherical shell are constructed in Cartesian coordinates terms elementary functions. Two scale-invariant equations defining two infinite series eigenvalues λ n and λ <m:m...