scholarly journals $L^\infty$-estimates for parabolic systems with VMO-coefficients

2010 ◽  
Vol 3 (2) ◽  
pp. 299-309 ◽  
Author(s):  
Horst Heck ◽  
◽  
Matthias Hieber ◽  
Kyriakos Stavrakidis
Keyword(s):  
Parabolic Systems ◽  
Vmo Coefficients

Orlicz Regularity for Non-Divergence Parabolic Systems with Partially Vmo Coefficients

2015 ◽  
Vol 116 (1) ◽  
pp. 141
Author(s):  
Maochun Zhu ◽  
Pengcheng Niu ◽  
Xiaojing Feng
Keyword(s):  
Strong Solutions ◽  
Parabolic Systems ◽  
Spatial Variables ◽  
Vmo Coefficients

This work treats the interior Orlicz regularity for strong solutions of a class of non-divergence parabolic systems with coefficients just measurable in time and VMO in the spatial variables.

$L^p-L^q$ ESTIMATES FOR PARABOLIC SYSTEMS IN NON-DIVERGENCE FORM WITH VMO COEFFICIENTS

2006 ◽  
Vol 74 (03) ◽  
pp. 717-736 ◽  
Author(s):  
ROBERT HALLER-DINTELMANN ◽  
HORST HECK ◽  
MATTHIAS HIEBER
Keyword(s):  
Parabolic Systems ◽  
Divergence Form ◽  
Vmo Coefficients

Stability in 𝐿𝑞-norm for inverse source parabolic problems

2020 ◽  
Vol 28 (6) ◽  
pp. 797-814
Author(s):  
Elena-Alexandra Melnig
Keyword(s):  
Parabolic Equations ◽  
Main Tool ◽  
Parabolic Systems ◽  
Carleman Estimates ◽  
Parabolic Problems ◽  
Lebesgue Spaces ◽  
First Order ◽  
Lipschitz Estimates ◽  
Systems Of Parabolic Equations

AbstractWe consider systems of parabolic equations coupled in zero and first order terms. We establish Lipschitz estimates in {L^{q}}-norms, {2\leq q\leq\infty}, for the source in terms of the solution in a subdomain. The main tool is a family of appropriate Carleman estimates with general weights, in Lebesgue spaces, for nonhomogeneous parabolic systems.

scholarly journals Lorentz spaces in action on pressureless systems arising from models of collective behavior

2021 ◽  
Author(s):  
Raphaël Danchin ◽  
Piotr Bogusław Mucha ◽  
Patrick Tolksdorf
Keyword(s):  
Initial Data ◽  
Collective Behavior ◽  
Existence And Uniqueness ◽  
Maximal Regularity ◽  
Parabolic Systems ◽  
Lorentz Spaces ◽  
Regularity Estimate ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Time Existence

AbstractWe are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the density is only bounded. Our results are based on interpolation and parabolic maximal regularity, where Lorentz spaces play a key role. We establish a novel maximal regularity estimate for parabolic systems in $$L_{q,r}(0,T;L_p(\Omega ))$$ L q , r ( 0 , T ; L p ( Ω ) ) spaces.

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