Gradient ranges of bumps on the plane
For a C1-smooth bump function b: ℝ2 → ℝ we show that the gradient range ∇ b(ℝ2) is the closure of its interior, provided that ∇b admits a modulus of continuity ω = ω(t) satisfying ω(t)√ → 0 as t ↘ 0. The result is a consequence of a more general result about gradient ranges of bump functions b: ℝn →...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2005
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