Hölder Continuity with Exponent (1 + Α)/2 in the Time Variable for Solutions of Parabolic Equations

نویسنده

  • JUNICHI ARAMAKI
چکیده

We consider the regularity of solutions for some parabolic equations. We show Hölder continuity with exponent (1 + α)/2, with respect to the time variable, when the gradient in the space variable of the solution has the Hölder continuity with exponent α.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Hölder Estimates for Solutions of Degenerate Nondivergence Elliptic and Parabolic Equations

We deal with a class of nondivergence type elliptic and parabolic equations degenerating at the coordinate hyperplanes. Assuming that the degeneration is coordinatewise and varies regularly, we prove the Hölder continuity of solutions. Also, the approximative solutions are considered. §

متن کامل

Hölder regularity for a non-linear parabolic equation driven by space-time white noise

Abstract. We consider the non-linear equation Tu+∂tu−∂ xπ(u) = ξ driven by space-time white noise ξ, which is uniformly parabolic because we assume that π′ is bounded away from zero and infinity. Under the further assumption of Lipschitz continuity of π′ we show that the stationary solution is — as for the linear case — almost surely Hölder continuous with exponent α for any α < 1 2 w. r. t. th...

متن کامل

On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions

We prove the interior Hölder continuity of weak solutions to parabolic systems ∂uj ∂t −Dαa α j (x, t, u,∇u) = 0 in Q (j = 1, . . . , N) (Q = Ω×(0, T ),Ω ⊂ R2), where the coefficients aj (x, t, u, ξ) are measurable in x, Hölder continuous in t and Lipschitz continuous in u and ξ.

متن کامل

Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition

‎Some functional inequalities‎ ‎in variable exponent Lebesgue spaces are presented‎. ‎The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non‎- ‎increasing function which is‎‎$$‎‎int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleq‎‎Cint_0^infty f(x)^{p(x)}u(x)dx‎,‎$$‎ ‎is studied‎. ‎We show that the exponent $p(.)$ for which these modular ine...

متن کامل

Local Bounds, Harnack’s Inequality and Hölder Continuity for Divergence Type Elliptic Equations with Non-standard Growth

We obtain a Harnack type inequality for solutions to elliptic equations in divergence form with non-standard p(x)-type growth. A model equation is the inhomogeneous p(x)-Laplacian. Namely, ∆p(x)u := div ( |∇u|p(x)−2∇u ) = f(x) in Ω, for which we prove Harnack’s inequality when f ∈ Lq0 (Ω) if max{1, N p1 } < q0 ≤ ∞. The constant in Harnack’s inequality depends on u only through ‖|u|p(x)‖p2−p1 L1...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015