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T. Adamowicz, and P. Hasto. (2009) "Mappings of finite distortion and PDE with nonstandard growth," International Mathematics Research Notices, Vol. 2009, Article ID rnn999, 15 pages.
 

Summary: T. Adamowicz, and P. H¨ast¨o. (2009) "Mappings of finite distortion and PDE with nonstandard growth,"
International Mathematics Research Notices, Vol. 2009, Article ID rnn999, 15 pages.
doi:10.1093/imrn/rnn999
Mappings of finite distortion and PDE with nonstandard growth
Tomasz wAdamowicz1
and Peter H¨ast¨o2
1
Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, OH
45221-0025, USA; adamowtz@ucmail.uc.edu; http://homepages.uc.edu/adamowtz/ and
2
Department of Mathematical Sciences, P.O. Box 3000, FI-90014 University of Oulu, Finland;
peter.hasto@helsinki.fi; http://cc.oulu.fi/phasto/
Correspondence to be sent to: peter.hasto@helsinki.fi
Quasiregular mappings with distortion K and solutions of the p-Laplace equation have both been recently extended to
the case where the parameter K or p is a function depending on the space variable. For the constant parameter case,
results by Bojarski­Iwaniec and Manfredi show that the gradient of a p-harmonic function in the plane is quasiregular
or constant. We generalize the result, showing that a planar p(·)-harmonic-type function, modeled on the strong
equation, is a mapping of finite distortion under appropriate assumptions.
1 Introduction
If u C2

  

Source: Adamowicz, Tomasz - Matematiska Institutionen, Linköpings Universitet

 

Collections: Mathematics