### Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space

Gubinelli M, Hofmanová M (2019)
Communications in Mathematical Physics 368(3): 1201-1266.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Gubinelli, Massimiliano; Hofmanová, MartinaUniBi
Einrichtung
Abstract / Bemerkung
We prove the existence of global solutions to singular SPDEs on Rd with cubic nonlinearities and additive white noise perturbation, both in the elliptic setting in dimensions d=4, 5 and in the parabolic setting for d = 2, 3. We prove uniqueness and coming down from infinity for the parabolic equations. A motivation for considering these equations is the construction of scalar interacting Euclidean quantum field theories. The parabolic equations are related to the phi d4 Euclidean quantum field theory via Parisi-Wu stochastic quantization, while the elliptic equations are linked to the phi d-24 Euclidean quantum field theory via the Parisi-Sourlas dimensional reduction mechanism.
Erscheinungsjahr
2019
Zeitschriftentitel
Communications in Mathematical Physics
Band
368
Ausgabe
3
Seite(n)
1201-1266
ISSN
0010-3616
eISSN
1432-0916
Page URI
https://pub.uni-bielefeld.de/record/2936016

### Zitieren

Gubinelli M, Hofmanová M. Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space. Communications in Mathematical Physics. 2019;368(3):1201-1266.
Gubinelli, M., & Hofmanová, M. (2019). Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space. Communications in Mathematical Physics, 368(3), 1201-1266. doi:10.1007/s00220-019-03398-4
Gubinelli, M., and Hofmanová, M. (2019). Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space. Communications in Mathematical Physics 368, 1201-1266.
Gubinelli, M., & Hofmanová, M., 2019. Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space. Communications in Mathematical Physics, 368(3), p 1201-1266.
M. Gubinelli and M. Hofmanová, “Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space”, Communications in Mathematical Physics, vol. 368, 2019, pp. 1201-1266.
Gubinelli, M., Hofmanová, M.: Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space. Communications in Mathematical Physics. 368, 1201-1266 (2019).
Gubinelli, Massimiliano, and Hofmanová, Martina. “Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space”. Communications in Mathematical Physics 368.3 (2019): 1201-1266.
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