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On the Agmon-Miranda maximum principle for solutions of strongly elliptic equations in domains of ℝn with conical points

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Abstract

In this paper the Agmon-Miranda maximum principle for solutions of strongly elliptic differential equations Lu = 0 in a bounded domain G with a conical point is considered. Necessary and sufficient conditions for the validity of this principle are given both for smooth solutions of the equation Lu = 0 in G and for the generalized solution of the problem Lu = 0 in G, D v k u = gk on ∂G (k = 0,...,m-1). It will be shown that for every elliptic operator L of order 2m > 2 there exists such a cone in ℝn (n≥4) that the Agmon-Miranda maximum principle fails in this cone.

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Authors and Affiliations

  1. Tekniska Högskolan i Linköping, Matematiska Institutionen, S-58183, Linköping, Sweden

    Vladimir G. Maz'ya

  2. Sektion Mathematik, Universität Rostock, Universitätsplatz 1, 2500, Rostock, Germany

    Jürgen Rossmann

Authors
  1. Vladimir G. Maz'ya
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  2. Jürgen Rossmann
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Communicated by B.W. Schulze

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Maz'ya, V.G., Rossmann, J. On the Agmon-Miranda maximum principle for solutions of strongly elliptic equations in domains of ℝn with conical points. Ann Glob Anal Geom 10, 125–150 (1992). https://doi.org/10.1007/BF00130916

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  • DOI: https://doi.org/10.1007/BF00130916

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