Extremal First Dirichlet Eigenvalue of Doubly Connected Plane Domains and Dihedral Symmetry
We deal with the following eigenvalue optimization problem: Given a bounded domain $D\subset {\bf R}^2$, place an obstacle $B$ of fixed shape within $D$ so as to maximize or minimize the fundamental ...
We deal with the following eigenvalue optimization problem: Given a bounded domain $D\subset {\bf R}^2$, place an obstacle $B$ of fixed shape within $D$ so as to maximize or minimize the fundamental ...
Weakly Coupled Schrödinger Operators on Regular Metric Trees
Spectral properties of the Schrödinger operator $ A_{\lambda} = -\Delta +\lambda V$ on regular metric trees are studied. It is shown that as $\lambda$ goes to zero the asymptotical behavior of t...
Spectral properties of the Schrödinger operator $ A_{\lambda} = -\Delta +\lambda V$ on regular metric trees are studied. It is shown that as $\lambda$ goes to zero the asymptotical behavior of t...
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A New Look at Equilibria in Stefan-Type Problems in the Plane
SIAM J. Math. Anal. Volume 39, Issue 4, pp. 1120-1134 (2007)
Published November 7, 2007
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We study steady states of Stefan-type problems in the plane with the Gibbs–Thomson correction involving a general anisotropic energy density function. By a local analysis we prove the global result showing that the solution is the Wulff shape. The key element is a stability result which enables us to approximate singular models by regular ones.
©2007 Society for Industrial and Applied Mathematics| History: | Received December 8, 2006; accepted July 24, 2007; published November 7, 2007 |
| Permalink: | http://dx.doi.org/10.1137/060677124 |
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0036-1410 (print)
1095-7154 (online)
SIAM