Papers by Peter Alexander
International Mathematics Research Notices, 2009
Quasiregular mappings with distortion K and solutions of the p-Laplace equation have both been re... more 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 Bojarski-Iwaniec 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.
In this article we study variable exponent Sobolev spaces on metric measure spaces. We employ two... more In this article we study variable exponent Sobolev spaces on metric measure spaces. We employ two definitions: a Haj lasz type definition, which uses a pointwise maximal inequality, and a Newtonian type definition, which uses an upper gradient. We prove that these spaces are Banach, that Lipschitz functions are dense as well as other basic properties. We also study when these spaces coincide.
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Papers by Peter Alexander