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Sobolev space

Sobolev embedding theorem

Hölder condition

Hölder space

{c}

On a ball of radius $R$, lower derivative norms of $u\in C^{l,\alpha}$ are bounded by an arbitrarily small multiple of the top Hölder seminorm plus a multiple of $\|u\|_{C^0}$. One endpoint form is
$$
R^l\|D^lu\|_0\leq\varepsilon R^{l+\alpha}[D^lu]_\alpha+C_\varepsilon\|u\|_0.
$$


Hölder interpolation inequality

Monotone iteration for a semilinear elliptic equation

Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 107 / 6 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 107 / 2 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 107 / 4 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 107 / 4 / c / ii / Solution

Hölder interpolation inequality

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Hölder interpolation inequality

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