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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
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vote
Showing coercivity condition for an energy functional
that is a good idea !
i guess that your conjecture may has a counter-example !
see : http://www.stanford.edu/class/math220b/handouts/calcvar.pdf
that is because :
$e(f, Q) \ge d ( \|Q\|^2_{W^{1,2} …