7 citations · 9 across the 4 of their papers we have counts for
5 papers
Homogeneous Solutions to Fully Nonlinear Elliptic Equations
Nikolai Nadirashvili, Yu Yuan
We classify homogeneous degree solutions to fully nonlinear elliptic equations.
Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond
Dmitry Jakobson, Michael Levitin, Nikolai Nadirashvili +1
Consider a bounded domain with the Dirichlet condition on a part of the boundary and the Neumann condition on its complement. Does the spectrum of the Laplacian determine uniquely…
Extremal metric for the first eigenvalue on a Klein bottle
Dmitry Jakobson, Nikolai Nadirashvili, Iosif Polterovich
The first eigenvalue of the Laplacian on a surface can be viewed as a functional on the space of Riemannian metrics of a given area. Critical points of this functional are called e…
Counterexamples for Local Isometric Embedding
Nikolai Nadirashvili, Yu Yuan
We construct smooth metrics on 2-manifold with nonpositive Gauss curvature which cannot be (C^3) locally isometrically embedded in R^3. Moreover, the Gauss curvature of the metric…
Linearity of homogeneous order one solutions to elliptic equations in dimension three
Qing Han, Nikolai Nadirashvili, Yu Yuan
We prove that any homogeneous order one solution to 3-d nondivergence elliptic equations must be linear.