We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in
has intrinsic cubic volume growth, provided the parametric elliptic integral is-close to the …

This is a survey of recent results on quantum ergodicity, specifically on the large energy
limits of matrix elements relative to eigenfunctions of the Laplacian. It is mainly devoted to …

The multiscale finite element method (MsFEM)[TY Hou, XH Wu, and Z. Cai, Math. Comp.,
1998, to appear; TY Hou and XH Wu, J. Comput. Phys., 134 (1997), pp. 169--189] has been …

Let M be a compact C^∞-smooth Riemannian manifold of dimension n, n≥3, and let
\varphi_λ=\Delta_M\varphi_λ+λ\varphi_λ=0 denote the Laplace eigenfunction on M …

Let u be a harmonic function in the unit ball B(0,1)⊂R^n, n≥3, such that u(0)=0. Nadirashvili
conjectured that there exists a positive constant c, depending on the dimension n only, such …

MEMOIRS Page 1 MEMOIRS of the American Mathematical Society Number 991 Q-Valued
Functions Revisited Camillo De Lellis Emanuele Nunzio Spadaro May 2011 • Volume 211 • …

In this paper, we introduce an inverse problem of a Schrödinger type variable nonlocal
elliptic operator (−∇⋅(A (x)∇)) s+ q), for 0< s< 1. We determine the unknown bounded …

Here we study the asymptotic limits of solutions of some singularly perturbed elliptic
systems. The limiting problems involve multiple valued harmonic functions or, in general …

An Optimal Partition Problem for Eigenvalues Page 1 DOI: 10.1007/s10915-006-9114-8
Journal of Scientific Computing, Vol. 31, Nos. 1/2, May 2007 (© 2006) An Optimal Partition …

Given a solution u to a linear, homogeneous, second‐order elliptic equation with Lipschitz
coefficients, we introduce techniques for giving improved estimates of the critical set 𝒷 (u) u …