Smooth local solutions to Weingarten equations and $\sigma_k$-equations
نویسندگان
چکیده
منابع مشابه
Solutions of Smooth Nonlinear Partial Differential Equations
and Applied Analysis 3 definition, it may happen that such a solution does not belong to any of the customary spaces of generalized functions. For example, given a function u : C \ {z0} −→ C 1.3 which is analytic everywhere except at the single point z0 ∈ C, and with an essential singularity at z0, Picard’s Theorem states that u attains every complex value, with possibly one exception, in every...
متن کاملSmooth approximations to solutions of nonconvex fully nonlinear elliptic equations
We show that fully nonlinear elliptic PDEs (which may not have classical solutions) can be approximated with integro-differential equations which have C solutions. For these approximated equation we prove a uniform C estimate. We also study the rate of convergence.
متن کاملSmooth Solutions to the 3D Navier-Stokes Equations Exist
In 1999, J.C. Mattingly and Ya. G. Sinai used elementary methods to prove the existence and uniqueness of smooth solutions to the 2D Navier-Stokes equations with periodic boundary conditions. And they were almost successful in proving the existence and uniqueness of smooth solutions to the 3D Navier-Stokes equations with periodic boundary conditions using the same strategy. In this paper, we mo...
متن کاملLocal and global nonexistence of solutions to semilinear evolution equations
For a fixed p and σ > −1, such that p > max{1, σ + 1}, one main concern of this paper is to find sufficient conditions for non solvability of ut = −(−∆) β 2 u− V (x)u+ th(x)u +W (x, t), posed in ST := R × (0, T ), where 0 < T < +∞, (−∆) β 2 with 0 < β ≤ 2 is the β/2 fractional power of the −∆, and W (x, t) = tw(x) ≥ 0. The potential V satisfies lim sup|x|→+∞ |V (x)||x| < +∞, for some positive a...
متن کاملLocal solutions for stochastic Navier Stokes equations
In this article we consider local solutions for stochastic Navier Stokes équations, based on the approach of Von Wahl, for the deterministic case. We present several approaches of the concept, depending on the smoothness available. When smoothness is available, we can in someway reduce the stochastic équation to a deterministic one with a random parameter. In the gênerai case, we mimic the conc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2015
ISSN: 1078-0947
DOI: 10.3934/dcds.2016.36.653