Number Theoretic Applications of Polynomials with Rational Coefficients Defined by Extremality Conditions

1983 ◽  
pp. 61-105 ◽  
Author(s):  
G. V. Chudnovsky
Keyword(s):  
Extremality Conditions

scholarly journals Extremality conditions for isolated and dynamical horizons

2008 ◽  
Vol 77 (8) ◽  
Author(s):  
Ivan Booth ◽  
Stephen Fairhurst
Keyword(s):  
Extremality Conditions

Limit Configurations of Schrödinger Systems Versus Optimal Partition for the Principal Eigenvalue of Elliptic Systems

2019 ◽  
Vol 19 (4) ◽  
pp. 693-715 ◽  
Author(s):  
Haijun Luo ◽  
Zhitao Zhang
Keyword(s):  
Principal Eigenvalue ◽  
Elliptic Systems ◽  
Coupling Constants ◽  
Optimal Partition ◽  
Minimizing Sequences ◽  
Linear Coupling ◽  
Existence Of Positive Solutions ◽  
Schrödinger Systems ◽  
Extremality Conditions ◽  
Schrödinger System

AbstractWe study a Schrödinger system of four equations with linear coupling functions and nonlinear couplings, including the case that the corresponding elliptic operators are indefinite. For any given nonlinear coupling {\beta>0}, we first use minimizing sequences on a normalized set to obtain a minimizer, which implies the existence of positive solutions for some linear coupling constants {\mu_{\beta},\nu_{\beta}} by Lagrange multiplier rules. Then, as {\beta\to\infty}, we prove that the limit configurations to the competing system are segregated in two groups, develop a variant of Almgren’s monotonicity formula to reveal the Lipschitz continuity of the limit profiles and establish a kind of local Pohozaev identity to obtain the extremality conditions. Finally, we study the relation between the limit profiles and the optimal partition for principal eigenvalue of the elliptic system and obtain an optimal partition for principal eigenvalues of elliptic systems.

Kolmogorov Decompositions and Extremality Conditions for Positive Covariant Kernels

2019 ◽  
Vol 83 (2) ◽  
pp. 253-271
Author(s):  
Erkka Haapasalo ◽  
Juha-Pekka Pellonpää
Keyword(s):  
Extremality Conditions
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