scholarly journals Feller semigroups and degenerate elliptic operators with Wentzell boundary conditions

2001 ◽  
Vol 145 (1) ◽  
pp. 17-53 ◽  
Author(s):  
Kazuaki Taira ◽  
Angelo Favini ◽  
Silvia Romanelli
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operators ◽  
Degenerate Elliptic Operators ◽  
Feller Semigroups ◽  
Wentzell Boundary Conditions ◽  
Degenerate Elliptic

Degenerate elliptic operators, Feller semigroups and modified Bernstein-Schnabl operators

2011 ◽  
Vol 284 (5-6) ◽  
pp. 587-607 ◽  
Author(s):  
Francesco Altomare ◽  
Mirella Cappelletti Montano ◽  
Sabrina Diomede
Keyword(s):  
Elliptic Operators ◽  
Degenerate Elliptic Operators ◽  
Feller Semigroups ◽  
Degenerate Elliptic

scholarly journals On some noncoercive variational inequalities containing degenerate elliptic operators

2003 ◽  
Vol 44 (3) ◽  
pp. 409-430
Author(s):  
Vy Khoi Le
Keyword(s):  
Boundary Conditions ◽  
Variational Inequalities ◽  
Elliptic Operators ◽  
Existence Results ◽  
Resonance Problem ◽  
Solution Existence ◽  
Degenerate Elliptic Operators ◽  
Degenerate Elliptic ◽  
Noncoercive Variational Inequalities

AbstractWe are concerned with the solvability of variational inequalities that contain degenerate elliptic operators. By using a recession approach, we find conditions on the boundary conditions such that the inequality has at least one solution. Existence results of Landesman-Lazer type for a nonsmooth inequality and a resonance problem for a weighted p-Laplacian are discussed in detail.

scholarly journals A class of strongly degenerate elliptic operators

1989 ◽  
Vol 39 (2) ◽  
pp. 177-200 ◽  
Author(s):  
Duong Minh Duc
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Elliptic Equations ◽  
Elliptic Operators ◽  
Regularity Of Solutions ◽  
Degenerate Elliptic Operators ◽  
Singular Elliptic Equations ◽  
Degenerate Elliptic ◽  
Weighted Poincaré Inequality ◽  
Strongly Degenerate

Using a weighted Poincaré inequality, we study (ω1,…,ωn)-elliptic operators. This method is applied to solve singular elliptic equations with boundary conditions in W1,2. We also obtain a result about the regularity of solutions of singular elliptic equations. An application to (ω1,…,ωn)-parabolic equations is given.

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.

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