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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 1999 • Question 13

Question

Math 6410 • ODE Fall 1999 • Question 13

Let \(G\) be an open set. Define the Sobolev spaces \(H^m(G)\), \(m=1,2,\ldots \), and \(H^m_0(G)\), \(m=1,2,\ldots \). Indicate why these spaces are Hilbert spaces.

Raw LaTeX

Let \(G\) be an open set. Define the Sobolev spaces \(H^m(G)\), \(m=1,2,\ldots\), and
\(H^m_0(G)\), \(m=1,2,\ldots\). Indicate why these spaces are Hilbert spaces.

Topic Tags

Hilbert Spaces and Orthogonality Sobolev Spaces and Energy Estimates