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Results tagged with ap.analysis-of-pdes
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user 126623
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
2
votes
1
answer
195
views
Estimate for the operator $A A_D^{-1}$
Let $O\subset\mathbb{R}^d$
be a bounded domain of the class $C^{1,1}$
(or $C^2$
for simplicity). Let the operator $A_D$
be formally given by the differential expression $A=-\operatorname{div}g(x)\nabl …
0
votes
Estimate for the operator $A A_D^{-1}$
From the identity $(AA_D^{-1}\phi,f)_{L_2}=(\phi,f)_{L_2}$ it follows that
$$\vert (\phi, (AA_D^{-1})^* f)_{L_2}\vert \leqslant \Vert \phi\Vert _{L_2}\Vert f\Vert _{L_2}\quad \forall \phi\in L_2(O).$$ …