# Measurable Semigroup Selection of the Heat Flow for Harmonic Maps

@inproceedings{Cardona2022MeasurableSS, title={Measurable Semigroup Selection of the Heat Flow for Harmonic Maps}, author={Jorge Eduardo Cardona}, year={2022} }

. J.-M. Coron proved in [5] that the global weak solutions of the heat ﬂow from M to N , starting at non-stationary weakly harmonic maps, are not unique when M = B 3 and N = S 2 . Hence, the semigroup property of the solution map does not hold in general. The present short paper uses the techniques developed by J. Cardona and L. Kapitanski to show the existence of inﬁnitely many measurable semigroups solving the heat ﬂow in the same cases where non-uniqueness was shown by J.-M. Coron.

## References

SHOWING 1-10 OF 11 REFERENCES

### Semiflow selection and Markov selection theorems

- MathematicsTopological Methods in Nonlinear Analysis
- 2020

The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup property arises…

### Heat Flows and Relaxed Energies for Harmonic Maps

- Mathematics
- 1992

In this paper we construct weak solutions for the heat flow associated with relaxed energies for harmonic maps between B3 and S2. Nonuniqueness results for such solutions are also given.

### The weak solutions to the evolution problems of harmonic maps

- Mathematics
- 1989

On demontre l'existence de solutions faibles globales a des problemes d'evolution des applications harmoniques de varietes de Riemann compactes (sans bord) dans des spheres

### Riemannian geometry and geometric analysis

- Mathematics
- 1995

* Established textbook
* Continues to lead its readers to some of the hottest topics of contemporary mathematical research
This established reference work continues to lead its readers to some of…

### ON THE SELECTION OF A MARKOV PROCESS FROM A SYSTEM OF PROCESSES AND THE CONSTRUCTION OF QUASI-DIFFUSION PROCESSES

- Mathematics
- 1973

In this paper the notion of a Markov system of processes is introduced, and it is proved that a Markov process can be selected from such a system. The usefulness of this fact is illustrated by the…