scholarly journals Analytic dependence on parameters for Evans' approximated Weak KAM solutions

2017 ◽  
Vol 37 (9) ◽  
pp. 4625-4636
Author(s):  
Olga Bernardi ◽  
◽  
Matteo Dalla Riva ◽  
Keyword(s):  
Analytic Dependence ◽  
Weak Kam Solutions ◽  
Analytic Dependence On Parameters

scholarly journals Existence results for a nonlinear nonautonomous transmission problem via domain perturbation

2021 ◽  
pp. 1-26
Author(s):  
Matteo Dalla Riva ◽  
Riccardo Molinarolo ◽  
Paolo Musolino
Keyword(s):  
Boundary Value Problem ◽  
Laplace Equation ◽  
Boundary Value ◽  
Perturbation Parameter ◽  
Existence Results ◽  
Transmission Problem ◽  
Perforated Domain ◽  
Analytic Dependence ◽  
Domain Perturbation ◽  
Fixed Domain

In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$ . First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$ .

scholarly journals Analytic Dependence of Orthogonal Polynomials

1991 ◽  
pp. 287-312 ◽  
Author(s):  
Enrico Laeng
Keyword(s):  
Orthogonal Polynomials ◽  
Analytic Dependence

Action potential and weak KAM solutions

2001 ◽  
Vol 13 (4) ◽  
pp. 427-458 ◽  
Author(s):  
Gonzalo Contreras
Keyword(s):  
Action Potential ◽  
Weak Kam Solutions

SOLITON SECTOR OF THE XY MODEL

1996 ◽  
Vol 10 (13n14) ◽  
pp. 1685-1693
Author(s):  
HUZIHIRO ARAKI
Keyword(s):  
Ground State ◽  
Point Spectrum ◽  
Single Point ◽  
Ground States ◽  
Finite Energy ◽  
Particle Energy ◽  
Xy Model ◽  
Analytic Dependence ◽  
Sudden Appearance ◽  
Infinite Multiplicity

We study soliton sectors of the XY model by using known results and methods about its ground states. In the regions of parameters for which ground states are not unique, we show that (1) there are two soliton sectors depending on parameters of the model analytically in a well-defined sense, (2) the only sectors with “finite energy” are ground state and soliton sectors, and (3) the sudden appearance of additional ground states at a pair of specific values of parameters (despite analytic dependence of other ground states on parameters at those specific values), which were found in earlier study of ground states, can be understood as the degeneracy of one particle energy in the soliton sector (which has a continuous spectrum at other values of parameters) to a single point spectrum with infinite multiplicity at the specific values of parameters.

scholarly journals Regularity of weak KAM solutions and Mañé’s Conjecture

2011 ◽  
pp. 1-22 ◽  
Author(s):  
Ludovic Rifford
Keyword(s):  
Weak Kam Solutions
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