Edge asymptotics on a skew cylinder: complex variable form
This paper is devoted to the study of the homogenization of a porous medium, composed of different materials arranged in a periodic structure. This provides the profile of the saturation function for the limit material.
We consider a class of eigenvalue problems for polyharmonic operators, including Dirichlet and buckling-type eigenvalue problems. We prove an analyticity result for the dependence of the symmetric functions of the eigenvalues upon domain perturbations and compute Hadamard-type formulas for the Frechét differentials. We also consider isovolumetric domain perturbations and characterize the corresponding critical domains for the symmetric functions of the eigenvalues. Finally, we prove that balls are...
Für die Lösungen seminlinearer parabolischer Differentialgleichungen werden Einschliessungsaussagen hergeleitet. Hierbei werden Aussagen zur Stabilität von Lösungen ermittelt. Die Resultate werden am Beispiel der Fitzhugh-Nagumo Gleichungen diskutiert.
In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class for all and, as a consequence, the Hölder regularity of the solution . is an elliptic second order operator with discontinuous coefficients and the lower order terms belong to suitable Lebesgue spaces.