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Results tagged with banach-spaces
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user 48485
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
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Semi-linear elliptic problem, energy functionals, Fréchet derivatives and the Newton method ...
Let me write out the equation $J''(u)w = g$ for $g\in H^{-1}$ and $w\in H^1_0(\Omega)$. This is equivalent to
$$
\int_\Omega \nabla w \cdot \nabla v - f''(u)wv = g(v) \quad \forall v\in H^1_0(\Omega). …
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