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CR submanifolds of maximal CR dimension of a complex space form with recurrent shape operator
Complex space form CR submanifold of maximal CR dimension
2011/2/28
Let M be a CR submanifold of maximal CR dimension of a complex space form M. The shape operator A of the distinguished vector field is recurrent if there exists a 1-form v such that ∇A = A X...
Are Some Optimal Shape Problems Convex?
optimal shape plate equation convexity maximal deformation beam
2009/2/5
The optimal shape problem in this paper is to construct plates or beams of minimal weight. The thickness $u(x)$ is variable, but the vertical deformation $y(x)$ should not exceed a certain threshhold....
Shape Optimization Problems over Classes of Convex Domains
Shape Optimization Problems Convex Domains
2009/2/5
We consider shape optimization problems of the form
\min\left\{\int_{\partial A} f(x,\nu(x))\hbox{d}x {\cal{H}^{n-1}} :A\in{\cal A}\right\}
where $f$ is any continuous function and the class ${\ca...
Dynamical Shape Control in Non-cylindrical Navier-Stokes Equations
Dynamical Shape Control Non-cylindrical Navier-Stokes Equations
2009/1/22
This paper deals with a dynamical shape control problem. The state equations are the non-cylindrical Navier-Stokes equations with a non-homogenous Dirichlet condition. The goal is to compute a necessa...
Lipschitz Continuity of the State Function in a Shape Optimization Problem
Lipschitz State Function Optimization Problem
2009/1/20
This paper deals with the existence and the regularity of state function $u$ in an $N$-dimensional shape optimization problem. We use a variational approach to get the existence of a solution $u$ of a...