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Math / Partial Differential Equations: An Introduction 2 / Chapter 7 / Problem 4

Partial Differential Equations: An Introduction | 2nd Edition | ISBN: 9780470054567 | Authors: Walter A. Strauss

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Verify directly from (3) that the solution has derivatives

Chapter 7, Problem 4

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QUESTION:

Verify directly from (3) that the solution has derivatives of all orders in {z > 0}. Assume that h(x, y) is a continuous function that vanishes outside some circle. (Hint: See Section A.3 for differentiation under an integral sign.)

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QUESTION:

Verify directly from (3) that the solution has derivatives of all orders in {z > 0}. Assume that h(x, y) is a continuous function that vanishes outside some circle. (Hint: See Section A.3 for differentiation under an integral sign.)

ANSWER:

Step 1 of 2

Assume that is a continuous function that vanishes outside the circle.

And,

Then,

U will possess derivatives if all order if exists.

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