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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 1997 • Question 20

Question

Math 6410 • ODE Fall 1997 • Question 20

Assume that \(u\in H^1(\mathbb {T}^n)\) is a weak solution to \(Lu=f(x)\) on \(\mathbb {T}^n\), where \(f\in C^\infty (\mathbb {T}^n)\). Show that \(u\in C^\infty (\mathbb {T}^n)\).

Raw LaTeX

Assume that \(u\in H^1(\T^n)\) is a weak solution to \(Lu=f(x)\) on \(\T^n\),
where \(f\in C^\infty(\T^n)\). Show that \(u\in C^\infty(\T^n)\).

Topic Tags

Distributions and Weak Solutions Entropy Solutions, Shocks, and Rarefactions Poincare Maps and Periodic Solutions Sobolev Spaces and Energy Estimates