Vertaisarvioitu alkuperäisartikkeli tai data-artikkeli tieteellisessä aikakauslehdessä (A1)
Maximal regularity for local minimizers of non-autonomous functionals
Julkaisun tekijät: Hästö Peter, Ok Jihoon
Kustantaja: EUROPEAN MATHEMATICAL SOC-EMS
Julkaisuvuosi: 2022
Journal: Journal of the European Mathematical Society
Tietokannassa oleva lehden nimi: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
Lehden akronyymi: J EUR MATH SOC
Volyymi: 24
Julkaisunumero: 4
Aloitussivu: 1285
Lopetussivun numero: 1334
Sivujen määrä: 50
ISSN: 1435-9855
DOI: http://dx.doi.org/10.4171/JEMS/1118
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/175031943
We establish local C-1;alpha-regularity for some alpha is an element of (0, 1) and C-alpha-regularity for any alpha is an element of (0, 1) of local minimizers of the functionalnu bar right arrow integral(Omega)phi(x, vertical bar D nu vertical bar)dx,where phi satisfies a(p, q)-growth condition. Establishing such a regularity theory with sharp, general conditions has been an open problem since the 1980s. In contrast to previous results, we formulate the continuity requirement on phi in terms of a single condition for the map(x, t) bar right arrow phi(x, t), rather than separately in the x- and t -directions. Thus we can obtain regularity results for functionals without assuming that the gap q=p between the upper and lower growth bounds is close to 1. Moreover, for phi(x, t) with particular structure, including p-, Orlicz-, p(x)- and double phasegrowth, our single condition implies known, essentially optimal, regularity conditions. Hence, we handle regularity theory for the above functional in a universal way.
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