Search results for "49Q10"
showing 5 items of 5 documents
Minimality via second variation for microphase separation of diblock copolymer melts
2017
Abstract We consider a non-local isoperimetric problem arising as the sharp interface limit of the Ohta–Kawasaki free energy introduced to model microphase separation of diblock copolymers. We perform a second order variational analysis that allows us to provide a quantitative second order minimality condition. We show that critical configurations with positive second variation are indeed strict local minimizers of the problem. Moreover, we provide, via a suitable quantitative inequality of isoperimetric type, an estimate of the deviation from minimality for configurations close to the minimum in the L 1 {L^{1}} -topology.
An elementary formula for computing shape derivatives of EFIE system matrix
2012
We derive analytical shape derivative formulas of the system matrix representing electric field integral equation discretized with Raviart-Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries of the original system matrix. The results are compared to derivatives computed with automatic differentiation technique and finite differences, and are found to be in excellent agreement.
Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants
2020
We provide a quantitative lower bound to the Cheeger constant of a set $\Omega$ in both the Euclidean and the Gaussian settings in terms of suitable asymmetry indexes. We provide examples which show that these quantitative estimates are sharp.
On the shape of compact hypersurfaces with almost constant mean curvature
2015
The distance of an almost constant mean curvature boundary from a finite family of disjoint tangent balls with equal radii is quantitatively controlled in terms of the oscillation of the scalar mean curvature. This result allows one to quantitatively describe the geometry of volume-constrained stationary sets in capillarity problems.
On the regularity of critical and minimal sets of a free interface problem
2015
We study a free interface problem of finding the optimal energy configuration for mixtures of two conducting materials with an additional perimeter penalization of the interface. We employ the regularity theory of linear elliptic equations to study the possible opening angles of Taylor cones and to give a different proof of a partial regularity result by Fan Hua Lin [Calc Var. Partial Differential Equations, 1993].