We are concerned with the problem of existence, uniqueness and qualitative properties of solutions to the radially symmetric variational problem \[ \min_{u\in\Wuu(B_R)}\int_{B_R} \pq{f\pt{\mod{x},\mod{\nabla u(x)}}+h(|x|,u(x))}\,dx, ~~~~~~~~~{ } \] where $B_R$ is the ball of $\R^n$ centered at the origin and with radius $R>0$, the map $f\colon [0,R]\times[0,+\infty[\to\Re$ is a normal integrand, and $h\colon[0,R]\times\R\to\R$ is a convex function of the second variable. %Neither convexity nor growth conditions are made on $f$. %In particular, $f$ is allowed to grow sub-linearly at infinity. This kind of problems, with non-convex lagrangians with respect to $\nabla u$, arise in various fields of applied sciences, such as optimal design and nonlinear elasticity.
Existence, uniqueness and qualitative properties of minima to radially symmetric noncoercive nonconvex variational problems / Crasta, Graziano. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 235(2000), pp. 569-589. [10.1007/s002090000148]
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Titolo: | Existence, uniqueness and qualitative properties of minima to radially symmetric noncoercive nonconvex variational problems | |
Autori: | ||
Data di pubblicazione: | 2000 | |
Rivista: | ||
Citazione: | Existence, uniqueness and qualitative properties of minima to radially symmetric noncoercive nonconvex variational problems / Crasta, Graziano. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 235(2000), pp. 569-589. [10.1007/s002090000148] | |
Handle: | http://hdl.handle.net/11573/67140 | |
Appartiene alla tipologia: | 01a Articolo in rivista |