What are some handy upper bounds for surface integrals (and their proofs)? Specifically, suppose $f$ is a bounded function on a surface $S$. Do we have $$ \int_{\partial S} F \cdot n \; \mathrm{d}S \leq m(\partial S) \sup_{x \in \partial S} F,$$ where $m(\,\cdot\,)$ is the Lebesgue measure? Cauchy Schwarz seems applicable.
2026-03-31 18:23:03.1774981383
Bounds on flux integrals
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