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Lavrentiev Phenomenon

Does there exist a (onedimensional) integral functional of calculus of variations $$ F(y)=\int_a^b f(t,y(t),y'(t))\,dt
 $$ such that not only $$ \inf_{y\in\operatorname{Lip}([a,b])}F(y)>\inf_{y\in ...
Carlo Mantegazza's user avatar
3 votes
0 answers
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Variational Principle for a System of Differential Equations

I am studying a differential operator of the form $$ L\left(\begin{array}{c} u \\ v \end{array}\right) = -\Delta \left(\begin{array}{c} u \\ v \end{array}\right) + V(x)\left(\begin{array}{c} u \\ v \...
k3thomps's user avatar
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2 votes
0 answers
64 views

The continuity of $L^2$ gradient on moving domain

I post this on MSE too. Sorry for this short cross posting. But I stuck in this problem for a while... I don't know what the right tool should be used to handle the moving domain problem... Let $I:=(...
JumpJump's user avatar
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