Existence of very weak solutions to elliptic systems of p-Laplacian type

  • Miroslav Bulíček
  • Sebastian SchwarzacherEmail author


We study vector valued solutions to non-linear elliptic partial differential equations with p-growth. Existence of a solution is shown in case the right hand side is the divergence of a function which is only q integrable, where q is strictly below but close to the duality exponent \(p'\). It implies that possibly degenerate operators of p-Laplacian type are well posed in a larger class then the natural space of existence. The key novelty here is a refined a priori estimate, that recovers a duality relation between the right hand side and the solution in terms of weighted Lebesgue spaces.

Mathematics Subject Classification

35D99 35J57 35J60 35A01 


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Mathematical Institute, Faculty of Mathematics and PhysicsCharles University in PraguePragueCzech Republic
  2. 2.Department of Mathematical Analysis, Faculty of Mathematics and PhysicsCharles University in PraguePragueCzech Republic

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