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Title of Journal: Potential Anal

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Abbravation: Potential Analysis

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Springer Netherlands

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10.1007/s11620-012-0163-8

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1572-929X

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On Calabi’s Strong Maximum Principle via Local Sem

Authors: Kazuhiro Kuwae
Publish Date: 2011/11/29
Volume: 37, Issue: 4, Pages: 387-413
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Abstract

We give a stochastic proof of an extension of E Calabi’s strong maximum principle under some geometric conditions in the framework of strong Feller diffusion processes associated to local regular semiDirichlet forms with lower bounds As a corollary our notion of subharmonicity implies a notion of viscosity subsolution in a stochastic sense We can apply our result to singular geometric object like Alexandrov space limit space under spectral distance of Riemannian manifolds with uniform lower Ricci curvature bound and so on

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  1. Maximal Inequalities of the Itô Integral with Respect to Poisson Random Measures or Lévy Processes on Banach Spaces
  2. Approximation of Invariant Measures for Regime-switching Diffusions
  3. Functional Inequalities and Hamilton–Jacobi Equations in Geodesic Spaces
  4. Brownian Motion and the Distance to a Submanifold
  5. Stability for Parabolic Quasiminimizers
  6. Complementability of Spaces of Harmonic Functions
  7. Equilibrium Diffusion on the Cone of Discrete Radon Measures
  8. Global Heat Kernel Estimates for Symmetric Markov Processes Dominated by Stable-Like Processes in Exterior C 1, η Open Sets
  9. Intertwining Relations for One-Dimensional Diffusions and Application to Functional Inequalities
  10. Integrals Along Rough Paths via Fractional Calculus
  11. Mosco Type Convergence of Bilinear Forms and Weak Convergence of n -Particle Systems
  12. Remarks on a Constrained Optimization Problem for the Ginibre Ensemble
  13. On States of Total Weighted Occupation Times of a Class of Infinitely Divisible Superprocesses on a Bounded Domain
  14. Uniqueness for Integro-PDE in Hilbert Spaces
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