scholarly journals Estimates of Dirichlet eigenvalues for a class of sub‐elliptic operators

2020 ◽  
Author(s):  
Hua Chen ◽  
Hong‐Ge Chen
Keyword(s):  
Elliptic Operators ◽  
Dirichlet Eigenvalues

Lower bounds of Dirichlet eigenvalues for a class of finitely degenerate Grushin type elliptic operators

2017 ◽  
Vol 37 (6) ◽  
pp. 1653-1664 ◽  
Author(s):  
Hua CHEN ◽  
Hongge CHEN ◽  
Yirui DUAN ◽  
Xin HU
Keyword(s):  
Lower Bounds ◽  
Elliptic Operators ◽  
Dirichlet Eigenvalues

scholarly journals Inequalities for the Navier and Dirichlet eigenvalues of elliptic operators

2011 ◽  
Vol 251 (1) ◽  
pp. 219-237 ◽  
Author(s):  
Qiaoling Wang ◽  
Changyu Xia
Keyword(s):  
Elliptic Operators ◽  
Dirichlet Eigenvalues

Lower and upper bounds of Dirichlet eigenvalues for totally characteristic degenerate elliptic operators

2014 ◽  
Vol 57 (11) ◽  
pp. 2235-2246 ◽  
Author(s):  
Hua Chen ◽  
RongHua Qiao ◽  
Peng Luo ◽  
DongYuan Xiao
Keyword(s):  
Upper Bounds ◽  
Elliptic Operators ◽  
Lower And Upper Bounds ◽  
Degenerate Elliptic Operators ◽  
Dirichlet Eigenvalues ◽  
Degenerate Elliptic

A computer-assisted proof method of the invertibility to elliptic operators

2014 ◽  
Vol 1 ◽  
pp. 816-819
Author(s):  
Akitoshi Takayasu ◽  
Shin'ichi Oishi
Keyword(s):  
Elliptic Operators ◽  
Computer Assisted ◽  
Computer Assisted Proof

Degenerate Diffusion Operators Arising in Population Biology (AM-185)

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Adjoint Operator ◽  
Integral Kernel ◽  
Mathematical Finance ◽  
Elliptic Operators ◽  
Complete Analysis ◽  
Time Behavior ◽  
Degenerate Elliptic Operators ◽  
Regularity Properties ◽  
Degenerate Elliptic ◽  
Mathematical Foundations

This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

About the G-compactness of certain classes of second-order elliptic operators

2018 ◽  
pp. 1-12
Author(s):  
Magomed Sirazhudinov ◽  
Saida Dzhamaludinova
Keyword(s):  
Elliptic Operators ◽  
Second Order ◽  
Second Order Elliptic Operators

scholarly journals Generalized principal eigenvalues of convex nonlinear elliptic operators in ℝN

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Anup Biswas ◽  
Prasun Roychowdhury
Keyword(s):  
Eigenvalue Problem ◽  
Principal Eigenvalue ◽  
Unbounded Domains ◽  
Elliptic Operators ◽  
Maximum Principles ◽  
Generalized Eigenvalues ◽  
Nonlinear Elliptic ◽  
Generalized Eigenvalue ◽  
General Convex ◽  
Appl Math

AbstractWe study the generalized eigenvalue problem in {\mathbb{R}^{N}} for a general convex nonlinear elliptic operator which is locally elliptic and positively 1-homogeneous. Generalizing [H. Berestycki and L. Rossi, Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains, Comm. Pure Appl. Math. 68 2015, 6, 1014–1065], we consider three different notions of generalized eigenvalues and compare them. We also discuss the maximum principles and uniqueness of principal eigenfunctions.

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