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

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

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whenever T>0 and . For the integrand f:Ω×RNn→[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

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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://dx.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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