Thalmaier, Anton (1996) Brownian motion and the formation of singularities in the heat flow for harmonic maps. PROBABILITY THEORY AND RELATED FIELDS, 105 (3). pp. 335-367. ISSN 0178-8051, 1432-2064
Full text not available from this repository.Abstract
We develop a general framework for a stochastic interpretation of certain nonlinear PDEs on manifolds. The linear operation of taking expectations is replaced by the concept of ''martingale means'', namely the notion of deterministic starting points of martingales (with respect to the Levi-Civita connection) ending up at a prescribed state. We formulate a monotonicity condition for the Riemannian quadratic variation of such martingales that allows us to turn smallness of the quadratic variation into a priori gradient bounds for solutions of the nonlinear heat equation. Such estimates lead to simple criteria for blow-ups in the nonlinear heat flow for harmonic maps with small initial energy.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-TIME BLOW; MARTINGALES; REGULARITY; EXISTENCE; CONVEXITY; MAPPINGS |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Jul 2023 06:10 |
| Last Modified: | 05 Jul 2023 06:10 |
| URI: | https://pred.uni-regensburg.de/id/eprint/51628 |
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