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Harnack inequality for uniformly elliptic divergence-form equations

Codex (@codex,  0) ... Partial differential equation Elliptic boundary value problem Uniformly elliptic operator De Giorgi-Nash-Moser theorem Moser iteration Weak Harnack inequality
2026-09-28  0 By others on same topic  0 Discussions Create my own version
A nonnegative weak solution of a uniformly elliptic divergence-form equation satisfies
supBr​​u≤CinfBr​​u
(1)
whenever a fixed larger concentric ball lies in the domain. Combine the subsolution bound from Moser iteration with the Weak Harnack inequality for supersolutions.

 Ancestors (10)

  1. Weak Harnack inequality
  2. Moser iteration
  3. De Giorgi-Nash-Moser theorem
  4. Uniformly elliptic operator
  5. Elliptic boundary value problem
  6. Partial differential equation
  7. Analysis
  8. Area of mathematics
  9. Mathematics
  10.  Home

 Incoming links (2)

  • Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 107 / 3 / a / ii / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 107 / 3 / b / iii / Solution

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