We study the regularity of the extremal solution of the semilinear biharmonic equation Î²âˆ†uâˆ’Ï„âˆ†u = Î» (1âˆ’u)2 on a ball B âŠ‚ R , under Navier boundary conditions u = âˆ†u = 0 on âˆ‚B, where Î» > 0 is aâ€¦ (More)

We give necessary and sufficient conditions on a pair of positive radial functions V and W on a ball B of radius R in R, n â‰¥ 1, so that the following inequalities hold for all u âˆˆ C 0 (B):

We study the regularity of the extremal solution of the semilinear biharmonic equation âˆ†u = Î» (1âˆ’u)2 , which models a simple Micro-Electromechanical System (MEMS) device on a ball B âŠ‚ R , underâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

2008

We give a necessary and sufficient condition on a radially symmetric potential V on a bounded domain Omega of (n) that makes it an admissible candidate for an improved Hardy inequality of theâ€¦ (More)

We consider the problem of recovering an isotropic conductivity outside some perfectly conducting or insulating inclusions from the interior measurement of the magnitude of one current density fieldâ€¦ (More)

Consider the problem ïš¾ âˆ†u = Î»e in B u = âˆ‚u âˆ‚n = 0 on âˆ‚B, where B is the unit ball in R and Î» is a parameter. Unlike the Gelfand problem the natural candidate u = âˆ’4 ln(|x|), for the extremalâ€¦ (More)

We give necessary and sufficient conditions on a pair of positive radial functions V and W on a ball B of radius R in R, n â‰¥ 1, so that the following inequalities hold for all u âˆˆ C 0 (B):

We study the regularity of the extremal solution of the semilinear biharmonic equation âˆ†u = Î» (1âˆ’u)2 , which models a simple Micro-Electromechanical System (MEMS) device on a ball B âŠ‚ R , underâ€¦ (More)