Abstract
We prove the local boundedness of variational solutions and parabolic minimizers to evolutionary problems, where the integrand f is convex and satisfies a non-standard p, q-growth condition with
A function \({u\colon \Omega_T := \Omega \times (0,T) \to \mathbb{R}}\) is called parabolic minimizer if it satisfies the minimality condition
for every \({\varphi \in C^\infty_0(\Omega_T)}\). Moreover, we will show local boundedness for parabolic minimizers, if f satisfies an anisotropic growth condition.
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Singer, T. Local boundedness of variational solutions to evolutionary problems with non-standard growth. Nonlinear Differ. Equ. Appl. 23, 19 (2016). https://doi.org/10.1007/s00030-016-0370-5
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DOI: https://doi.org/10.1007/s00030-016-0370-5