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Results tagged with ap.analysis-of-pdes
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user 530631
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
4
votes
1
answer
79
views
Tangential Sobolev spaces
Let $\Omega \subset \mathbf R^n$ be a smooth domain and define $U_s=\{x\in\Omega \mid d(x,\partial \Omega)<s\}$;
let $f\in W^{1,p}(\Omega)∩W_{\mathrm{loc}} ^{2,p}(\Omega)$;
let $v$ be the unit normal …
0
votes
0
answers
14
views
Characterization of duals of Sobolev space
Proposition 8.14. in Brezis states that:$(W_0^{1,p} (Ω))^*=W^{-1,p^*} (Ω)$ and we have the representation:
$∀ F∈(W_0^{1,p} (Ω))^* ∃ f_0...f_n ∈L^{p^*} (Ω)$ such that $∀ u∈W_0^{1,p}(Ω)$
$F(u)=∫_Ω uf …