搜索结果: 1-9 共查到“偏微分方程 E-sets”相关记录9条 . 查询时间(0.114 秒)
PRINCIPAL CURVATURE ESTIMATES FOR THE CONVEX LEVEL SETS OF SEMILINEAR ELLIPTIC EQUATIONS
PRINCIPAL CURVATURE ESTIMATES THE CONVEX LEVEL SETS SEMILINEAR ELLIPTIC EQUATIONS
2014/4/3
We give a positive lower bound for the principal curvature of the strict convex level sets of harmonic functions in terms of the principal curvature of the domain boundary and the norm of the boundary...
Semiclassical resolvent estimates at trapped sets
Resolvent estimates trapping propagation of singularities
2012/6/21
We extend our recent results on propagation of semiclassical resolvent estimates through trapped sets when a priori polynomial resolvent bounds hold. Previously we obtained non-trapping estimates in t...
Anisotropic covering of fractal sets
Anisotropic covering of fractal sets Pattern Formation and Solitons
2012/4/26
We consider the optimal covering of fractal sets in a two-dimensional space using ellipses which become increasingly anisotropic as their size is reduced. If the semi-minor axis is \epsilon and the se...
A natural lower bound for the size of nodal sets
natural lower bound size of nodal sets Analysis of PDEs
2011/9/14
Abstract: We prove a natural inequality which implies the known lower bounds for the $(n-1)$-dimensional Hausdorff measure of nodal sets for smooth compact manifolds.
Dimension of attractors and invariant sets of damped wave equations in unbounded domains
damped wave equation invariant set attractor dimension
2011/9/5
Abstract: Under fairly general assumptions, we prove that every compact invariant set $\mathcal I$ of the semiflow generated by the semilinear damped wave equation u_{tt}+\alpha u_t+\beta(x)u-\Deltau ...
Lower bounds for volumes of nodal sets: an improvement of a result of Sogge-Zelditch
Lower bounds volumes of nodal sets Sogge-Zelditch
2011/8/22
Abstract: We use the Dong-Sogge-Zelditch formula to obtain a lower bound for the volume of the nodal sets of eigenfunctions. Our result improves the recent results of Sogge-Zelditch and in dimensions ...
Fractal curvature measures and Minkowski content for one-dimensional self-conformal sets
Fractal curvature measures Minkowski one-dimensional self-conformal sets
2011/2/28
We investigate intrinsic geometric properties of invariant sets of one-dimensional conformal iterated function systems. We show that for such a set F the fractal cur-vature measures exist, if and only...
Coincidence sets in quasilinear elliptic problems of monostable type
Coincidence sets quasilinear elliptic problems of monostable type
2010/12/7
This paper concerns the formation of a coincidence set for the positive solution of the boundary value problem: −"pu = uq−1 f (a(x)−u) in with u = 0 on @ , where " is a positive pa...
For a large class of self-similar sets F in Rd, analogues of the higher order mean curvatures
of differentiable submanifolds are introduced, in particular, the fractal Gauss-type curvature.
They are...