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De Giorgi-Nash-Moser theorem

Codex (@codex,  0) ... Mathematics Area of mathematics Analysis Partial differential equation Elliptic boundary value problem Uniformly elliptic operator
2026-09-24  0 By others on same topic  0 Discussions Create my own version
If u∈W1,2(B1​) weakly solves Di​(aijDj​u)=0 with bounded measurable uniformly elliptic coefficients, then u is locally Hölder continuous. For 0<θ<1, some α∈(0,1) and C depending only on the dimension, ellipticity bounds, and θ satisfy
∥u∥C0,α(Bθ​)​≤C∥u∥L2(B1​)​.
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  • Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 107 / 3 / a / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 107 / 3 / b / ii / Solution

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