32,138 research outputs found
An Interior Estimate for a Nonlinear Parabolic Equation
In this paper there are estimated the derivatives of the solution of an
initial boundary value problem for a nonlinear uniformly parabolic equation in
the interior with the total variation of the boundary data and the
L^{infinity}-norm of the initial condition.Comment: 16 page
Ground states in complex bodies
A unified framework for analyzing the existence of ground states in wide
classes of elastic complex bodies is presented here. The approach makes use of
classical semicontinuity results, Sobolev mappinngs and Cartesian currents.
Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev
maps and Cartesian currents describe the inner substructure of the material
elements. Balance equations for irregular minimizers are derived. A
contribution to the debate about the role of the balance of configurational
actions follows. After describing a list of possible applications of the
general results collected here, a concrete discussion of the existence of
ground states in thermodynamically stable quasicrystals is presented at the
end.Comment: 30 pages, in print on ESAIM-COC
Elementary quotient completion
We extend the notion of exact completion on a weakly lex category to
elementary doctrines. We show how any such doctrine admits an elementary
quotient completion, which freely adds effective quotients and extensional
equality. We note that the elementary quotient completion can be obtained as
the composite of two free constructions: one adds effective quotients, and the
other forces extensionality of maps. We also prove that each construction
preserves comprehensions
Solitary waves for Maxwell-Schrodinger equations
In this paper we study the solitary waves for the coupled Schr\"odinger -
Maxwell equations in three-dimensional space. We prove the existence of a
sequence of radial solitary waves for these equations with a fixed norm.
We study the asymptotic behavior and the smoothness of these solutions. We show
also the fact that the eigenvalues are negative and the first one is isolated.Comment: 31 page
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