Asymptotic Behavior of the Solution of an Elliptic Pseudo-Differential Equation Near a Cone



We consider the equation
$$(Au_{+})(x) = f(x), \quad x \in C^a_+,$$
where A is a pseudo-differential operator with symbol A(ξ) satisfying the condition
$$c_1 \leq |A(\xi)(1 + |\xi|)^{-\alpha}| \leq c_2, \quad \forall\xi \in \mathbb{R}^m,$$
and \(C^a_+\) is the cone \(\{x \in \mathbb{R}^m: x_m > a| x^\prime |, x^{\prime} = (x_1, \ldots , x_{m-1}), a > 0\}\).


Asymptotic Behavior Asymptotic Expansion Integral Operator Convolution Operator Basic Formula 
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© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Bryansk State UniversityBryanskRussia

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