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- W2265584329 abstract "We consider evolutionary problems associated with a convex integrand $${f : Omega_T times {mathbb R}^{Nn} to [0, infty)}$$ , which is $${alpha}$$ -Hölder continuous with respect to the x-variable and satisfies a non-standard p, q-growth condition. We prove the existence of weak solutions $${u : Omega_T to {mathbb R}^N}$$ , which solve $$partial_{t} u - {rm div} partial_{zeta} f(x, t, Du) = 0$$ weakly in $${Omega_{T}}$$ . Therefore, we use the concept of variational solutions, which exist under a mild assumption on the gap q − p, namely $$frac{2n}{n+2} < p leq q < p + 1.$$ For $$frac{2n}{n+2} < p leq q < p + frac{{rm min}{2, p} alpha}{n+2},$$ we prove that the spatial derivative Du of a variational solution u admits a higher integrability and is accordingly a weak solution." @default.
- W2265584329 created "2016-06-24" @default.
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- W2265584329 date "2016-02-12" @default.
- W2265584329 modified "2023-10-02" @default.
- W2265584329 title "Existence of weak solutions of parabolic systems with p, q-growth" @default.
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- W2265584329 doi "https://doi.org/10.1007/s00229-016-0827-1" @default.
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