# Laplacian

(1) Show u belongs to C^1(U), and calculate ux, uy.

(2) Calculate uxx, uyy, uxy and show that uxx and uyy are continuous in the whole disk, but u does not belong to C^2. Calculate f := - delta u.

Please see the attached image for complete question.

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#### Solution Summary

Continuous calculations are displayed in the solution.

$2.19