Journal
ADVANCES IN NONLINEAR ANALYSIS
Volume 9, Issue 1, Pages 710-728Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/anona-2020-0022
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Funding
- PRIN 2017
- Ministry of Education and Science of the Russian Federation (5-100 program of the Russian Ministry of Education)
- Japan Society for the Promotion of Science KAKENHI [17K05337]
- Grants-in-Aid for Scientific Research [17K05337] Funding Source: KAKEN
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The functionals of double phase type H(u) := integral (vertical bar Du vertical bar(p)+ a(x)vertical bar Du vertical bar(q)) dx, (q > p > 1, a(x) >= 0) are introduced in the epoch-making paper by Colombo-Mingione [1] for constants p and q, and investigated by them and Baroni. They obtained sharp regularity results for minimizers of such functionals. In this paper we treat the case that the exponents are functions of x and partly generalize their regularity results.
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