Manuscripta Mathematica

, Volume 138, Issue 3–4, pp 287–298 | Cite as

On continuity properties of monotone operators beyond the natural domain of definition

  • Miroslav Bulíček


We study boundary value problems associated to a nonlinear elliptic system of partial differential equations. The leading second order elliptic operator provides L 2-coerciveness and has at most linear growth with respect to the gradient. Incorporating properties of Lipschitz approximations of Sobolev functions we are able to show that the problems in consideration are well-posed, in the sense of Hadamard, in W 1,p for all \({p \in (p_0,2]}\) for certain \({p_0 \in [3/2,2)}\) . For simplicity we restrict ourselves to the Dirichlet problem.

Mathematics Subject Classification (2000)

35J45 35J66 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics and Physics, Mathematical InstituteCharles UniversityPrague 8Czech Republic

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