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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 1999 • Question 12

Question

Math 6410 • ODE Fall 1999 • Question 12

Provide the higher dimensional analogue of the previous exercise, i.e., let \[ r:\mathbb {R}^N\to \mathbb {R} \] be defined by \[ r(x)=1,\quad \lvert x\rvert <1, \qquad r(x)=0,\quad \lvert x\rvert \ge 1. \] Compute the distributional gradient \(\nabla r\) of \(r\).

Raw LaTeX

Provide the higher dimensional analogue of the previous exercise, i.e., let
\[
  r:\R^N\to\R
\]
be defined by
\[
  r(x)=1,\quad \lvert x\rvert<1,
  \qquad
  r(x)=0,\quad \lvert x\rvert\ge1.
\]
Compute the distributional gradient \(\nabla r\) of \(r\).

Topic Tags

Distributions and Weak Solutions