scholarly journals On conormal derivative problem for parabolic equations with Dini mean oscillation coefficients

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hongjie Dong ◽  
Xinghong Pan
Keyword(s):  
Parabolic Equations ◽  
Derivative Problem ◽  
Mean Oscillation

Estimates for parabolic equations with measure data in generalized Morrey spaces

2019 ◽  
Vol 21 (05) ◽  
pp. 1850044
Author(s):  
Chao Zhang
Keyword(s):  
Parabolic Equations ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Parabolic Problems ◽  
Measure Data ◽  
Spatial Gradient ◽  
Irregular Domain ◽  
Variable Formula ◽  
Mean Oscillation ◽  
Morrey Estimates

In this paper, we prove the optimal generalized Morrey estimates for the spatial gradient of the solutions obtained by limits of approximations (SOLA) for a class of parabolic problems with right-hand side measure in a very general irregular domain. The nonlinearity is assumed to be merely measurable only in the time variable [Formula: see text] and belongs to the small bounded mean oscillation (BMO) class as functions of the spatial variable [Formula: see text].

Generalized Morrey Regularity for Parabolic Equations with Discontinuous Data

2014 ◽  
Vol 58 (1) ◽  
pp. 199-218 ◽  
Author(s):  
Vagif S. Guliyev ◽  
Lubomira G. Softova
Keyword(s):  
Parabolic Equations ◽  
Regularity Result ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Bmo Functions ◽  
Mean Oscillation ◽  
Sublinear Operators ◽  
Vmo Coefficients ◽  
Morrey Regularity ◽  
Discontinuous Data

AbstractWe prove continuity in generalized parabolic Morrey spacesof sublinear operators generated by the parabolic Calderón—Zygmund operator and by the commutator of this operator with bounded mean oscillation (BMO) functions. As a consequence, we obtain a global-regularity result for the Cauchy—Dirichlet problem for linear uniformly parabolic equations with vanishing mean oscillation (VMO) coefficients.

scholarly journals The Uniformly Parabolic Equations of Higher Order with Discontinuous Data in Generalized Morrey Spaces and Elliptic Equations in Unbounded Domains

2021 ◽  
Author(s):  
Tair Gadjiev ◽  
Konul Suleymanova
Keyword(s):  
Parabolic Equations ◽  
Unbounded Domains ◽  
Morrey Spaces ◽  
Higher Order ◽  
Bounded Mean Oscillation ◽  
Bmo Functions ◽  
Mean Oscillation ◽  
Sublinear Operators ◽  
Vmo Coefficients ◽  
Discontinuous Data

We study the regularity of the solutions of the Cauchy-Dirichlet problem for linear uniformly parabolic equations of higher order with vanishing mean oscillation (VMO) coefficients. We prove continuity in generalized parabolic Morrey spaces Mp,φ of sublinear operators generated by the parabolic Calderon-Zygmund operator and by the commutator of this operator with bounded mean oscillation (BMO) functions. We obtain strong solution belongs to the generalized Sobolev-Morrey space Wp,φm,1∘Q. Also we consider elliptic equation in unbounded domains.

WEIGHTED SOLVABILITY FOR PARABOLIC EQUATIONS WITH PARTIALLY BMO COEFFICIENTS AND ITS APPLICATIONS

2014 ◽  
Vol 96 (3) ◽  
pp. 396-428
Author(s):  
LIN TANG
Keyword(s):  
Bounded Domain ◽  
Parabolic Equations ◽  
Global Regularity ◽  
Morrey Spaces ◽  
Divergence Form ◽  
Bounded Mean Oscillation ◽  
Nondivergence Form ◽  
Mean Oscillation ◽  
Bmo Coefficients

AbstractWe consider the weighted $L_p$ solvability for divergence and nondivergence form parabolic equations with partially bounded mean oscillation (BMO) coefficients and certain positive potentials. As an application, global regularity in Morrey spaces for divergence form parabolic operators with partially BMO coefficients on a bounded domain is established.

scholarly journals Gradient weighted norm inequalities for very weak solutions of linear parabolic equations with BMO coefficients

2021 ◽  
pp. 1-15
Author(s):  
Le Trong Thanh Bui ◽  
Quoc-Hung Nguyen
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Lipschitz Constant ◽  
Weighted Norm ◽  
Very Weak Solutions ◽  
Class A ◽  
Mean Oscillation ◽  
Muckenhoupt Class ◽  
Linear Parabolic Equations ◽  
Bmo Coefficients

In this paper, we give a short proof of the Lorentz estimates for gradients of very weak solutions to the linear parabolic equations with the Muckenhoupt class A q -weights u t − div ( A ( x , t ) ∇ u ) = div ( F ) , in a bounded domain Ω × ( 0 , T ) ⊂ R N + 1 , where A has a small mean oscillation, and Ω is a Lipchistz domain with a small Lipschitz constant.

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