When does the free boundary enter into corner points of the fixed boundary?
When is a pseudo-differential equation solvable ?
This paper begins with a broad survey of the state of the art in matters of solvability for differential and pseudo-differential equations. Then we proceed with a Hilbertian lemma which we use to prove a new solvability result.
When is the first eigenfunction for the clamped plate equation of fixed sign?
Which electric fields are realizable in conducting materials?
In this paper we study the realizability of a given smooth periodic gradient field ∇u defined in Rd, in the sense of finding when one can obtain a matrix conductivity σ such that σ∇u is a divergence free current field. The construction is shown to be always possible locally in Rd provided that ∇u is non-vanishing. This condition is also necessary in dimension two but not in dimension three. In fact the realizability may fail for non-regular gradient fields, and in general the conductivity cannot...
Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?
In this paper we give a general presentation of the homogenization of Neumann type problems in periodically perforated domains, including the case where the shape of the reference hole varies with the size of the period (in the spirit of the construction of self-similar fractals). We shows that -convergence holds under the extra assumption that there exists a bounded sequence of extension operators for the reference holes. The general class of Jones-domains gives an example where this result applies....
Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?
In this paper we give a general presentation of the homogenization of Neumann type problems in periodically perforated domains, including the case where the shape of the reference hole varies with the size of the period (in the spirit of the construction of self-similar fractals). We shows that H0-convergence holds under the extra assumption that there exists a bounded sequence of extension operators for the reference holes. The general class of Jones-domains gives an example where this result...
Which solutions of the third problem for the Poisson equation are bounded?
Whitham averaged equations and modulational stability of periodic traveling waves of a hyperbolic-parabolic balance law
In this note, we report on recent findings concerning the spectral and nonlinear stability of periodic traveling wave solutions of hyperbolic-parabolic systems of balance laws, as applied to the St. Venant equations of shallow water flow down an incline. We begin by introducing a natural set of spectral stability assumptions, motivated by considerations from the Whitham averaged equations, and outline the recent proof yielding nonlinear stability under these conditions. We then turn to an analytical...
Whitney elements on pyramids.
Wiener criterion for degenerate elliptic obstacle problem
We give a Wiener criterion for the continuity of an obstacle problem relative to an elliptic degenerate problem with a weight in the class.
Wiener type algebras of pseudodifferential operators
Wiener's Criterion in Potential Theory with Applications to Nilpotent Lie Groups.
Wiener's test of thinness in potential theory
Wigner series and (semi)classical limits with periodic potentials
WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity
Wm,2-Fehlerabschätzungen für Galerkin-Näherungen schwach elliptischer quasilinearer Randwertprobleme 2m-ter Ordnung.
Worst scenario method in homogenization. Linear case
The paper deals with homogenization of a linear elliptic boundary problem with a specific class of uncertain coefficients describing composite materials with periodic structure. Instead of stochastic approach to the problem, we use the worst scenario method due to Hlaváček (method of reliable solution). A few criterion functionals are introduced. We focus on the range of the homogenized coefficients from knowledge of the ranges of individual components in the composite, on the values of generalized...
Wüst's Theorem and Positively Perturbed Schrödinger Operators.