Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 119-162

ELLIPTIC INTERPOLATION ESTIMATES FOR NON-STANDARD GROWTH OPERATORS

Paolo Baroni and Jens Habermann

Uppsala University, Department of Mathematics
Lägerhyddsvägen 1, SE-751 06, Uppsala, Sweden; paolo.baroni 'at' math.uu.se

Universität Erlangen, Department Mathematik
Cauerstr. 11, 91058 Erlangen, Germany, habermann 'at' math.fau.de

Abstract. We derive a class of potential estimates for elliptic equations with non-standard growth having a measure on the right-hand side; in particular our results allow to interpolate between the pointwise estimates available for solutions to this equation and the ones for the gradient. We allow bounded coefficients in BMO and VMO classes.

2010 Mathematics Subject Classification: Primary 35J15, 35J60, 35J99.

Key words: Non-standard growth conditions, Wolff and Riesz potentials, pointwise estimates.

Reference to this article: P. Baroni and J. Habermann: Elliptic interpolation estimates for non-standard growth operators. Ann. Acad. Sci. Fenn. Math. 39 (2014), 119-162.

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doi:10.5186/aasfm.2014.3915