We consider embedded hypersurfaces evolving by fully nonlinear flows in which the normal speed of motion is a homogeneous degree one, concave or convex function of the principal curvatures, and prove a noncollapsing estimate: Precisely, the function which gives the curvature of the largest interior sphere touching the hypersurface at each point is a subsolution of the linearized flow equation i...

We investigate fully nonlinear, non-Abelian excitations of quark-antiquark plasma, using relativistic fluid theory in cold plasma approximation. There are mainly three important nonlinearities, coming from various sources such as non-Abelian interactions of Yang-Mills (YM) fields, Wong’s color dynamics and plasma nonlinearity, in our model. By neglecting nonlinearities due to plasma and color d...

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth...

We get existence, uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of Hamilton-Jacobi-BellmanIsaacs type, with unbounded ingredients and quadratic growth in the gradient, without hypotheses of convexity or properness. Some of our results are new even for equations in divergence form.

We prove that the existence of a solution to a fully nonlinear elliptic equation in a bounded domain Ω with an overdetermined boundary condition prescribing both Dirichlet and Neumann constant data forces the domain Ω to be a ball. This is a generalization of Serrin’s classical result from 1971.

This paper studies the averaging problem for some fully nonlinear equations of degenerate parabolic type with a Hamiltonian not necessarily periodic in the fast variable. Our aim is to point out a sufficient condition on the Hamiltonian to pass to the limit in the starting equation. Also, we investigate when this condition is not completely fulfilled and discuss some examples concerning determi...

An exact numerical scheme for a long-term simulation of three-dimensional potential fully-nonlinear periodic gravity waves is suggested. The scheme is based on a surfacefollowing non-orthogonal curvilinear coordinate system and does not use the technique based on expansion of the velocity potential. The Poisson equation for the velocity potential is solved iteratively. The Fourier transform met...

In this paper, we introduce and study quotients of fully nonlinear control systems. Our definition is inspired by categorical definitions of quotients as well as recent work on abstractions of affine control systems. We show that quotients exist under mild regularity assumptions and characterize the structure of the quotient state/input space. This allows one to understand how states and inputs...