The Fundamental Solution of a Linear Elliptic Differential Equation with Analytic Coefficients

Fritz John
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Fritz John: New York University, Courant Institute of Mathematical Sciences

Chapter Chapter III in Plane Waves and Spherical Means, 1981, pp 43-76 from Springer

Abstract: Abstract Denote by L[u] a differential operator of the form (3.1) L [ u ] = ∑ k = 0 m ∑ i 1 , .. , i k = 1 , ... , n A i 1 ... i k ( x ) ∂ k u ∂ x i 1 ... ∂ x i k $$L[u]\, = \,\sum\limits_{k = 0}^m {\,\,\sum\limits_{\begin{array}{*{20}{c}} {{i_1},..,{i_k}} \\ { = 1,...,n} \end{array}} {\,\,{A_{{i_1}}}{{...}_i}_{_k}} } \,(x)\,\frac{{{\partial ^k}u}}{{\partial {x_{{i_1}}}...\partial {x_{{i_k}}}}}$$ .

Keywords: Cauchy Problem; Plane Wave; Fundamental Solution; Elliptic Operator; Regular Solution (search for similar items in EconPapers)
Date: 1981
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DOI: 10.1007/978-1-4613-9453-2_4

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