Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222514 | Nonlinear Analysis: Theory, Methods & Applications | 2018 | 28 Pages |
Abstract
The objects of our studies are vector valued parabolic minimizers u associated to a convex Carathéodory integrand f obeying a p-growth assumption from below and a certain monotonicity condition in the gradient variable. Here, the functions being considered are defined on a metric measure space (X,d,μ). For such parabolic minimizers that coincide with a time-independent Cauchy-Dirichlet datum u0 on the parabolic boundary of a space-time-cylinder ΩÃ(0,T) with an open subset ΩâX and T>0, we prove existence in the parabolic Newtonian space Lp(0,T;N1,p(Ω;RN)). In this paper we generalize results from Bögelein et al. (2014,2015) to the metric setting and argue completely on a variational level.
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Authors
Michael Collins, Andreas Herán,