Gap Phenomenon for Some Autonomous FunctionalsGiovanni
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چکیده
We give an example of an autonomous functional F (u) = R f (u; Du)dx ((open subset of IR 2 , u : ! IR 2 in the Sobolev space W 1;1) which is sequentially weakly lower semicontinuous in W 1;p for every p 1 but does not agree with the relaxation of the same functional restricted to smooth functions when p < 2. A Lavrentiev phenomenon occurs for a related boundary problem.
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تاریخ انتشار 1994