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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 1997 • Question 17

Question

Math 6410 • ODE Fall 1997 • Question 17

Find a condition relating \(\Omega \) and \(V\) which implies there exists a unique weak solution \(u\in H^1_0(\Omega )\) for problem (6). Prove the existence and uniqueness under your condition.

Raw LaTeX

Find a condition relating \(\Omega\) and \(V\) which implies there exists a
unique weak solution \(u\in H^1_0(\Omega)\) for problem (6). Prove the existence and
uniqueness under your condition.

Topic Tags

Distributions and Weak Solutions Existence and Uniqueness Theorems Global Existence and Finite-Time Blow-Up Sobolev Spaces and Energy Estimates