I need to show that there exist a bounded domain $ \Omega \subset \mathbb{R}^2 $, and a Dirichlet eigenfunction $u$ on $ \Omega$ such that u cannot be extended to a continuous function on $ \bar{\Omega}$ (closure).
2025-01-12 23:39:24.1736725164
Dirichlet eigenfunction cannot be extended to a continuous function on the closure
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