Gradient weighted norm inequalities for very weak solutions of linear parabolic equations with BMO coefficients
نویسندگان
چکیده
In this paper, we give a short proof of the Lorentz estimates for gradients very weak solutions to linear parabolic equations with Muckenhoupt class A q -weights u t − div ( x , ) ∇ = F in bounded domain Ω × 0 T ⊂ R N + 1 where has small mean oscillation, and is Lipchistz Lipschitz constant.
منابع مشابه
Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients
We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the leading coefficients are measurable in one variable and have small BMO semi-norms in the other variables, variable exponents p(x) satisfy log-Hölder continuity, and the boundarie...
متن کاملExistence of Solutions for Degenerate Parabolic Equations with Rough Coefficients
We prove that a sequence of quasi-solutions to non-degenerate degenerate parabolic equations with rough coefficients is strongly Lloc-precompact. The result is obtained using the H-measures and a new concept of quasihomogeneity. A consequence of the precompactness is existence of a weak solution to the equation under consideration.
متن کاملNonlinear Equations and Weighted Norm Inequalities
We study connections between the problem of the existence of positive solutions for certain nonlinear equations and weighted norm inequalities. In particular, we obtain explicit criteria for the solvability of the Dirichlet problem −∆u = v u + w, u ≥ 0 on Ω, u = 0 on ∂Ω, on a regular domain Ω in Rn in the “superlinear case” q > 1. The coefficients v, w are arbitrary positive measurable function...
متن کامل-Weighted Inequalities with Lipschitz and BMO Norms
Copyright q 2010 Yuxia Tong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We first define a new kind of A λ3 r λ 1 , λ 2 , ΩΩ two-weight, then obtain some two-weight integral inequalities with Lipschitz norm and BMO norm ...
متن کاملReal Analytic Solutions of Parabolic Equations with Time-measurable Coefficients
We use Bernstein’s technique to show that for any fixed t, strong solutions u(t, x) of the uniformly parabolic equation Lu := aij (t)uxixj−ut = 0 in Q are real analytic in Q(t) = {x : (t, x) ∈ Q}. Here, Q ⊂ Rd+1 is a bounded domain and the coefficients aij(t) are measurable. We also use Bernstein’s technique to obtain interior estimates for pure second derivatives of solutions of the fully nonl...
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: Asymptotic Analysis
سال: 2022
ISSN: ['0921-7134', '1875-8576']
DOI: https://doi.org/10.3233/asy-211693