Lu, Li-jiang A uniqueness theorem for the first boundary value problems of linear elliptic and parabolic equations with discontinuous boundary values. (Chinese) Zbl 0154.36603 Acta Math. Sin. 15, 372-385 (1965). The author examines the question of uniqueness of solutions of the standard Dirichlet problems for second order elliptic and parabolic equations when the data are discontinuous on the boundary. A typical result is the following: Let \( \Omega \) denote a bounded domain in \( R^{n} \) with boundary \( \sigma \) and let \( \mathscr{E} \subset \sigma \) denote a set of zero Lebesgue measure. We denote by \( L \) a second order elliptic operator for which the standard maximum principle holds. If \( \Omega \) satisfies certain geometric conditions and \( u(x) \) is a bounded continuous solution on \( \bar{\Omega} \delta \) of the problem \( L u=0, x \in \Omega, u=0, x \in \sigma / \delta \) then \( u \equiv 0 \) for \( x \in \bar{\Omega} / \mathcal{E} \). - Similar results are obtained for solutions of parabolic equations with discontinuous initial data. Results for unbounded solutions are also obtained. This review text is based on a scanned copy of the printed version. It was converted to LaTeX using MathPix and a specifically developed LLM to assign the text parts to the metadata. It may contain errors, misassignments, or gaps; in particular, the reviewer signature has not yet been extracted reliably in general. If you notice any errors, please report them directly to our editorial team via the Contact Form. Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 Documents Keywords:partial differential equations × Cite Format Result Cite Review PDF