Higher integrability for parabolic systems with non-standard growth and degenerate diffusions
By Verena Bogelein, Frank Duzaar. 2011
68 citations recorded by the source corpus.
The aim of this paper is to establish a Meyer's type higher integrability result for weak solutions of possibly degenerate parabolic systems of the type ∂t u│- div ɑ ( x, t, D u) = div (│F│p (x,t) – 2 F). The vector-field a is assumed to fulfill a non-standard p(x; t)- growth condition. In particular it is shown that there exists Є > 0 depending only on the structural data such that there holds: │Du│p(·)(1+є) ∈ L1/loc together with a local estimate for the p(·) (1 + ɛ)-energy.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/e5f1a3ec28445c6ff8e7f5593a899212ece7a520
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In Applied Mathematics
- Paolo Baroni
- Verena Bogelein
- Giuseppe Mingione
- Frank Duzaar
- Andrea Cianchi
- Tuomo Kuusi
- Vladimir G. Maz'ya
- Patrick Winkert
In Computational Theory and Mathematics
- Paolo Baroni
- Verena Bogelein
- Giuseppe Mingione
- Frank Duzaar
- Andrea Cianchi
- Vladimir G. Maz'ya
- Tuomo Kuusi
- Patrick Winkert
Citations in the corpus
- Hölder estimates for parabolic p(x, t)-Laplacian systems (2012, background): “5) from [9], i.”
- Calderón–Zygmund estimates for parabolic p(x,t)-Laplacian systems (2014, background): “This result was first established in the case of the p(x, t)-Laplacian equation by Antontsev and Zhikov [9], and later for a quite general class of parabolic systems with p(x, t)-growth independently by Zhikov and Pastukhova [34] and Bögelein and Duzaar [10].”