Partial Differential Equations

V. V. Volchkov
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V. V. Volchkov: Donetsk National University, Department of Mathematics

Chapter Chapter 7 in Integral Geometry and Convolution Equations, 2003, pp 46-48 from Springer

Abstract: Abstract Let $$ \mathcal{U} $$ be a non-empty open subset of ℝ n . Consider the differential operator 7.1 $$ P = P\left( {x,\partial } \right) = \sum\limits_{\left| \alpha \right| \leqslant m} {c_\alpha \left( x \right)\partial ^\alpha } , $$ where c α ∈ RA( $$ \mathcal{U} $$ ). For (x,ξ) ∈ $$ \mathcal{U} $$ × ℝ n we set $$ P_m \left( {x,\xi } \right) = \sum\limits_{\left| \alpha \right| = m} {c_\alpha \left( x \right)\xi ^\alpha } $$ . We denote Char $$ P = \left\{ {\left( {x,\xi } \right) \in \mathcal{U} \times \left( {\mathbb{R}^n \backslash \left\{ 0 \right\}} \right):P_m \left( {x,\xi } \right) = 0} \right\} $$ . We say that P is elliptic on $$ \mathcal{U} $$ if CharP = Ø.

Keywords: Integral Equation; Partial Differential Equation; Fourier Analysis; Differential Operator; Harmonic Function (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-010-0023-9_7

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DOI: 10.1007/978-94-010-0023-9_7

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