Bögelein V, Habermann J (2010)
Publication Type: Journal article
Publication year: 2010
Publisher: Academia Scientiarum Fennica
Book Volume: 35
Pages Range: 641-678
URI: http://www.acadsci.fi/mathematica/Vol35/BogeleinHabermann.html
We consider elliptic problems with non standard growth conditions whose most prominent model example is the p(x)-Laplacean equation with a measure data right-hand side μ. We prove pointwise gradient estimates in terms of a non standard version of the non-linear Wolff potential of the right-hand side measure, and moreover a characterization for C1-regularity of the solution, also in terms of the Wolff potential. The C1-regularity criterion is also related to the density of μ and the decay rate of its L"-norm on small balls. Moreover, from the pointwise gradient estimates the Calderón and Zygmund theory and several types of local estimates follow as a consequence.
APA:
Bögelein, V., & Habermann, J. (2010). Gradient estimates via non standard potentials and continuity. Annales Academiae Scientiarum Fennicae-Mathematica, 35, 641-678. https://dx.doi.org/10.5186/aasfm.2010.3541
MLA:
Bögelein, Verena, and Jens Habermann. "Gradient estimates via non standard potentials and continuity." Annales Academiae Scientiarum Fennicae-Mathematica 35 (2010): 641-678.
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