Existence of evolutionary variational solutions via the calculus of variations

Bögelein V, Duzaar F, Marcellini P (2014)

Publication Status: Published

Publication Type: Journal article

Publication year: 2014

Journal

Journal of Differential Equations Elsevier

Publisher: Elsevier

Book Volume: 256

Pages Range: 3912-3942

Journal Issue: 12

DOI: 10.1016/j.jde.2014.03.005

Abstract

In this paper we introduce a purely variational approach to time dependent problems, yielding the existence of global parabolic minimizers, that is

whenever T>0 $T > 0$ and $φ \in C_{0}^{\infty} (Ω \times (0, T), R^{N})$ . For the integrand f:Ω×R^Nn→[0,∞] we merely assume convexity with respect to the gradient variable and coercivity. These evolutionary variational solutions are obtained as limits of maps depending on space and time minimizing certain convex variational functionals. In the simplest situation, with some growth conditions on f, the method provides the existence of global weak solutions to Cauchy–Dirichlet problems of parabolic systems of the type

$_{}$

Authors with CRIS profile

Verena Anna Maria Bögelein Naturwissenschaftliche Fakultät Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

Università degli Studi di Firenze / University of Florence

Italy (IT)

How to cite

APA:

Bögelein, V., Duzaar, F., & Marcellini, P. (2014). Existence of evolutionary variational solutions via the calculus of variations. Journal of Differential Equations, 256(12), 3912-3942. https://doi.org/10.1016/j.jde.2014.03.005

MLA:

Bögelein, Verena, Frank Duzaar, and Paolo Marcellini. "Existence of evolutionary variational solutions via the calculus of variations." Journal of Differential Equations 256.12 (2014): 3912-3942.

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