The method of moving planes and the sliding method are used in proving monotonicity or
symmetry in, say, the x 1 direction for solutions of nonlinear elliptic equations F (x, u, Du, D 2 …

This book is the written and somewhat expanded version of the author's lectures delivered at
the NSF-CBMS international research conference organized at the Mathematics Department …

Analyzing a free boundary problem for harmonic functions in an infinite planar domain, we
prove that in a solitary water wave each particle is transported in the wave direction but …

This book presents the basic theory of the symmetry of solutions to second-order elliptic
partial differential equations by means of the maximum principle. It proceeds from …

I~ l-+ w Since then there have been lots of works published in this direction treating a variety
of symmetry problems.(See eg [BN1, 2, 3],[CGS],[CL],[CN],[CS],[FL],[L],[LN1, 2, 3].) Generally …

This survey covers the mathematical theory of steady water waves with an emphasis on
topics that are at the forefront of current research. These areas include: variational …

Publisher Summary This chapter explains some qualitative properties of semilinear elliptic
equations in cylindrical domains. In studying differential equations, it is often of interest to …

SYMMETRY OF STEADY PERIODIC GRAVITY WATER WAVES WITH VORTICITY Page 1
SYMMETRY OF STEADY PERIODIC GRAVITY WATER WAVES WITH VORTICITY ADRIAN …

In this paper, we prove the mean-convex neighborhood conjecture for neck singularities of
the mean curvature flow in R n+ 1 for all n≥ 3: we show that if a mean curvature flow {M t} in …

This book is a self-contained introduction to the theory of periodic, progressive, permanent
waves on the surface of incompressible inviscid fluid. The problem of permanent water …