51,602 research outputs found
The p-Laplace equation in domains with multiple crack section via pencil operators
The p-Laplace equation
\n \cdot (|\n u|^n \n u)=0 \whereA n>0, in a bounded domain \O \subset
\re^2, with inhomogeneous Dirichlet conditions on the smooth boundary \p \O
is considered. In addition, there is a finite collection of curves
\Gamma = \Gamma_1\cup...\cup\Gamma_m \subset \O, \quad \{on which we assume
homogeneous Dirichlet boundary conditions} \quad u=0, modeling a multiple
crack formation, focusing at the origin 0 \in \O. This makes the above
quasilinear elliptic problem overdetermined. Possible types of the behaviour of
solution at the tip 0 of such admissible multiple cracks, being a
"singularity" point, are described, on the basis of blow-up scaling techniques
and a "nonlinear eigenvalue problem". Typical types of admissible cracks are
shown to be governed by nodal sets of a countable family of nonlinear
eigenfunctions, which are obtained via branching from harmonic polynomials that
occur for . Using a combination of analytic and numerical methods,
saddle-node bifurcations in are shown to occur for those nonlinear
eigenvalues/eigenfunctions.Comment: arXiv admin note: substantial text overlap with arXiv:1310.065
Holography, Pade Approximants and Deconstruction
We investigate the relation between holographic calculations in 5D and the
Migdal approach to correlation functions in large N theories. The latter
employs Pade approximation to extrapolate short distance correlation functions
to large distances. We make the Migdal/5D relation more precise by quantifying
the correspondence between Pade approximation and the background and boundary
conditions in 5D. We also establish a connection between the Migdal approach
and the models of deconstructed dimensions.Comment: 28 page
Form Factors for Integrable Lagrangian Field Theories, the Sinh-Gordon Model
Using Watson's and the recursive equations satisfied by matrix elements of
local operators in two-dimensional integrable models, we compute the form
factors of the elementary field and the stress-energy tensor
of Sinh-Gordon theory. Form factors of operators with higher
spin or with different asymptotic behaviour can easily be deduced from them.
The value of the correlation functions are saturated by the form factors with
lowest number of particle terms. This is illustrated by an application of the
form factors of the trace of to the sum rule of the
-theorem.Comment: 40 page
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