scholarly journals Manifolds Without Green’s Formula

1972 ◽  
Vol 45 ◽  
pp. 129-138
Author(s):  
Moses Glasner
Keyword(s):  
Differential Equations ◽  
Weak Solutions ◽  
Harmonic Functions ◽  
Green’S Formula ◽  
Global Properties ◽  
Green's Formula

Recently attention has been focused on manifolds that carry covariant tensors that are merely bounded measurable. In terms of these tensors global differential equations are defined and their weak solutions are called harmonic functions. Nakai initiated the classification of these manifolds with respect to the global properties of the harmonic functions that they carry.

scholarly journals Global properties of Dirichlet forms in terms of Green’s formula

2017 ◽  
Vol 56 (5) ◽  
Author(s):  
Sebastian Haeseler ◽  
Matthias Keller ◽  
Daniel Lenz ◽  
Jun Masamune ◽  
Marcel Schmidt
Keyword(s):  
Dirichlet Forms ◽  
Green’S Formula ◽  
Global Properties ◽  
Green's Formula

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

scholarly journals Limit Behavior of Solutions of Ordinary Linear Differential Equations

1994 ◽  
Vol 1 (3) ◽  
pp. 315-323
Author(s):  
František Neuman
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Linear Differential Equations ◽  
Limit Behavior ◽  
Limit Sets ◽  
Equivalent Linear ◽  
Linear Differential ◽  
Ordinary Linear Differential Equations

Abstract A classification of classes of equivalent linear differential equations with respect to ω-limit sets of their canonical representatives is introduced. Some consequences of this classification to the oscillatory behavior of solution spaces are presented.

scholarly journals Boundary Regularity for p-Harmonic Functions and Solutions of Obstacle Problems on Unbounded Sets in Metric Spaces

2019 ◽  
Vol 7 (1) ◽  
pp. 179-196
Author(s):  
Anders Björn ◽  
Daniel Hansevi
Keyword(s):  
Harmonic Functions ◽  
Obstacle Problem ◽  
Metric Spaces ◽  
Local Property ◽  
Boundary Regularity ◽  
Obstacle Problems ◽  
Regular Boundary ◽  
Complete Metric Spaces ◽  
Regularity Results

Abstract The theory of boundary regularity for p-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a p-Poincaré inequality, 1 < p < ∞. The barrier classification of regular boundary points is established, and it is shown that regularity is a local property of the boundary. We also obtain boundary regularity results for solutions of the obstacle problem on open sets, and characterize regularity further in several other ways.

Sign in / Sign up

Export Citation Format

Share Document