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

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

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, Dkvu = 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.

J. Roßmann | V. Maz'ya | Jürgen Rossmann | Vladimir G. Maz'ya

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