Gevrey Hypoellipticity for Partial Differential Equations with Characteristics of Higher Multiplicity
نویسنده
چکیده
We consider a class of partial differential equations with characteristics of constant multiplicity m ≥ 4. We prove for these equations a result of hypoellipticity and Gevrey hypoellipticity, by using classical Fourier integral operators and Sm ρ,δ arguments.
منابع مشابه
The Gevrey hypoellipticity for a class of kinetic equations
In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations without an angular cutoff.
متن کاملUnique Continuation and Complexity of Solutions to Parabolic Partial Differential Equations with Gevrey Coefficients
In this paper, we provide a quantitative estimate of unique continuation (doubling property) for higher-order parabolic partial differential equations with non-analytic Gevrey coefficients. Also, a new upper bound is given on the number of zeros for the solutions with a polynomial dependence on the coefficients.
متن کاملOn the Gevrey Analyticity of Solutions of Semilinear Perturbations of Powers of the Mizohata Operator
We consider the Gevrey hypoellipticity of nonlinear equations with multiple characteristics, consisting of powers of the Mizohata operator and a Gevrey analytic nonlinear perturbation. The main theorem states that under some conditions on the perturbation every H s solution (with s ≥ s0) of the equation is a Gevrey function. To prove the result we do not use the technique of cut-off functions, ...
متن کاملThe Gevrey Hypoellipticity for Linear and Non-linear
In this paper, we study the Gevrey regularity of weak solution for a class of linear and semilinear Fokker-Planck equations.
متن کاملIntermediate Optimal Gevrey Exponents Occur
Hypoellipticity in Gevrey classesG is characterized for a simple family of sums of squares of vector fields satisfying the bracket hypothesis, with analytic coefficients. It is shown that hypoellipticity holds if and only if s is greater than or equal to an optimal exponent that may take on any rational value.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000