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

V. B. Vasilyev ()
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V. B. Vasilyev: Bryansk State University

Chapter 28 in Integral Methods in Science and Engineering, Volume 1, 2010, pp 301-305 from Springer

Abstract: Abstract 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 $$\{x \in \mathbb{R}^m: x_m > a| x^\prime |, x^{\prime} = (x_1, \ldots , x_{m-1}), a > 0\}$$ .

Keywords: Asymptotic Behavior; Asymptotic Expansion; Integral Operator; Convolution Operator; Basic Formula (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-0-8176-4899-2_28

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