Approximations by regular sets and Wiener solutions in metric spaces

Anders Björn; Jana Björn

Displaying similar documents to “Approximations by regular sets and Wiener solutions in metric spaces”

On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator $W_{k} : = Δ + \frac{k}{x_{n}} \frac{\partial}{\partial x_{n}}$ on $ℝ^{n}$ is proved. In this note there is shown that in the cases $k \neq 0$ , $k \neq 2$ no other transforms of this kind exist and for case $k = 2$ , all such transforms are described.

Completely regular spaces

H. L. Bentley, Eva Lowen-Colebunders (1991)

Commentationes Mathematicae Universitatis Carolinae

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We conduct an investigation of the relationships which exist between various generalizations of complete regularity in the setting of merotopic spaces, with particular attention to filter spaces such as Cauchy spaces and convergence spaces. Our primary contribution consists in the presentation of several counterexamples establishing the divergence of various such generalizations of complete regularity. We give examples of: (1) a contigual zero space which is not weakly regular and is...

Asymptotics for the minimization of a Ginzburg-Landau energy in n dimensions

Paweł Strzelecki (1996)

Colloquium Mathematicae

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We prove that minimizers $u \in W^{1, n}$ of the functional $E_{} (u) = 1 / n \int_{|} {\nabla u |}^{n} d x + 1 / (4^{n}) \int_{(} 1 - {| u |}^{2})^{2} d x$ , ⊂ $ℝ^{n}$ , n ≥ 3, which satisfy the Dirichlet boundary condition $u_{} = g$ on for g: → $S^{n - 1}$ with zero topological degree, converge in $W^{1, n}$ and $C_{l o c}^{α}$ for any α<1 - upon passing to a subsequence $_{k} \to 0$ - to some minimizing n-harmonic map. This is a generalization of an earlier result obtained for n=2 by Bethuel, Brezis, and Hélein. An example of nonunique asymptotic behaviour (which cannot occur in two dimensions if deg g = 0) is presented.

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

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We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification...