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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 1993 • Question 11

Question

Math 6410 • ODE Fall 1993 • Question 11

Evaluate \(\Delta _3(1/r^2)\), \(r^2=x^2+y^2+z^2\) in \(\mathbb {R}^3\), where \(\Delta _3\) is the distributional Laplacian.

Raw LaTeX

Evaluate \(\Delta_3(1/r^2)\), \(r^2=x^2+y^2+z^2\) in \(\R^3\), where
\(\Delta_3\) is the distributional Laplacian.

Topic Tags

Distributions and Weak Solutions Fundamental Solutions Laplace Equation