3. Let A denote the Laplace operator, viz., a²f8²f Af := + əx² əy² Here f = f(x, y). The second order PDE Af = 0, which is the same as a²f8²f + 0, əx² dy² is called the Laplace equation. Any solution f = f(x, y) of the Laplace equation is called a harmonic function. Show that the function ln(x² + y²), (x, y) = (0,0) is harmonic.

3. Let A denote the Laplace operator, viz., a²f8²f Af := + əx² əy² Here f = f(x, y). The second order PDE Af = 0, which is the same as a²f8²f + 0, əx² dy² is called the Laplace equation. Any solution f = f(x, y) of the Laplace equation is called a harmonic function. Show that the function ln(x² + y²), (x, y) = (0,0) is harmonic.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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