Higher integrability for parabolic systems with Orlicz growth
نویسندگان
چکیده
We prove higher integrability of the spatial gradient weak solutions to parabolic systems with $\phi$-growth, where $\varphi=\varphi(t)$ is a general Orlicz function. The need be neither degenerate nor singular. Our result generalized version one J. Kinnunen and Lewis [Duke Math. 102 (2000), no. 2, 253--271] for $p$-Laplace systems.
منابع مشابه
Higher Integrability for Parabolic Systems with Non-standard Growth and Degenerate Diffusions
(1.1) ∂tu− div a(z,Du) = div ( |F |p(z)−2F ) in ΩT . Here, ΩT denotes the space time cylinder Ω × (0, T ) over a bounded domain Ω ⊆ R with dimension n ≥ 2. We write z = (x, t) for points in R, Du for the spatial gradient of u and ∂tu for the derivative with respect to time. The function u : ΩT → R with N ≥ 1 can possibly be vector valued, so that we include in our considerations the case of par...
متن کاملHIGHER INTEGRABILITY FOR PARABOLIC SYSTEMS OF p-LAPLACIAN TYPE
it is known that solutions locally belong to a slightly higher Sobolev space than assumed a priori. This self-improving property was first observed by Elcrat and Meyers in [ME] (see also [Gi] and [Str]). Their argument is based on reverse Hölder inequalities and a modification of Gehring’s lemma [Ge], which originally was developed to study the higher integrability of the Jacobian of a quasicon...
متن کاملHigher Integrability for Weak Solutions of Higher Order Degenerate Parabolic Systems
We consider a class of higher order nonlinear degenerate parabolic systems, whose easiest model is the parabolic p-Laplacean system ∫ ΩT ( u · φt − |Dmu|p−2Dmu ·Dmφ ) dz = ∫
متن کاملHigher Integrability for Solutions to Parabolic Problems with Irregular Obstacles and Nonstandard Growth
The aim of this paper is to derive the self-improving property of integrability for the spatial gradient of solutions to degenerate parabolic obstacle problem with irregular obstacles and p(x, t)-nonstandard growth. More precisely, we prove that the spatial gradient of the solution is integrable to a larger power than the natural one determined by the structural assumptions on the involved di e...
متن کاملIntegrability Conditions Pertaining to Orlicz Space
Recently S. Tikhonov proved two theorems on the integrability of sine and cosine series with coefficients from the R 0 BV S class. These results are extended such that the R 0 BV S class is replaced by the MRBV S class.
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: Journal of Differential Equations
سال: 2021
ISSN: ['1090-2732', '0022-0396']
DOI: https://doi.org/10.1016/j.jde.2021.08.012