منابع مشابه
On Nodal Lines of Neumann Eigenfunctions
We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain.
متن کاملOn Nodal Lines of Neumann Eigenfunctions
We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain.
متن کاملCounting nodal domains
We consider the nodal domains of Gaussian random waves in two dimensions. We present a method to calculate the distribution of the number of nodal domains and the average connectivity with the help of auxiliary Potts-spins. An analytical approach could be helpful to decide whether the pattern of nodal domains belongs to the universality class of short-ranged percolation. This is not completely ...
متن کاملThe Neumann Problem on Lipschitz Domains
Au — 0 in D; u = ƒ on bD9 where ƒ and its gradient on 3D belong to L(do). For C domains, these estimates were obtained by A. P. Calderón et al. [1]. For dimension 2, see (d) below. In [4] and [5] we found an elementary integral formula (7) and used it to prove a theorem of Dahlberg (Theorem 1) on Lipschitz domains. Unknown to us, this formula had already been discovered long ago by Payne and We...
متن کاملOn Neumann Eigenfunctions in Lip Domains
A planar set D will be called a lip domain if it is Lipschitz, open, bounded, connected, and given by (1) D = {(x1, x2) : f1(x1) < x2 < f2(x1)}, where f1, f2 are Lipschitz functions with constant 1. The assumption that D is a Lipschitz domain puts an extra constraint on the functions fk; we discuss this issue in greater detail later in this section. Let μ2 denote the second eigenvalue for the L...
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ژورنال
عنوان ژورنال: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2014
ISSN: 1364-503X,1471-2962
DOI: 10.1098/rsta.2012.0505