scholarly journals Higher integrability for parabolic systems with Orlicz growth

2021 ◽  
Vol 300 ◽  
pp. 925-948
Author(s):  
Peter Hästö ◽  
Jihoon Ok
Keyword(s):  
Parabolic Systems ◽  
Higher Integrability

Higher integrability for parabolic systems of p -Laplacian type

2000 ◽  
Vol 102 (2) ◽  
pp. 253-271 ◽  
Author(s):  
Juha Kinnunen ◽  
John L. Lewis
Keyword(s):  
Parabolic Systems ◽  
Higher Integrability

scholarly journals Higher integrability results for non smooth parabolic systems: The subquadratic case

2009 ◽  
Vol 11 (1) ◽  
pp. 177-190
Author(s):  
Chiara Leone ◽  
◽  
Anna Verde ◽  
Giovanni Pisante ◽  
Keyword(s):  
Parabolic Systems ◽  
Higher Integrability

scholarly journals Higher integrability near the initial boundary for nonhomogeneous parabolic systems of 𝑝-Laplacian type

2020 ◽  
Vol 32 (6) ◽  
pp. 1539-1559
Author(s):  
Sun-Sig Byun ◽  
Wontae Kim ◽  
Minkyu Lim
Keyword(s):  
Weak Solution ◽  
Type System ◽  
Regularity Theory ◽  
Structural Data ◽  
Parabolic Systems ◽  
Initial Boundary ◽  
Optimal Regularity ◽  
Higher Integrability ◽  
Regularity Results ◽  
Higher Regularity

AbstractWe establish a sharp higher integrability near the initial boundary for a weak solution to the following p-Laplacian type system:\left\{\begin{aligned} \displaystyle u_{t}-\operatorname{div}\mathcal{A}(x,t,% \nabla u)&\displaystyle=\operatorname{div}\lvert F\rvert^{p-2}F+f&&% \displaystyle\phantom{}\text{in}\ \Omega_{T},\\ \displaystyle u&\displaystyle=u_{0}&&\displaystyle\phantom{}\text{on}\ \Omega% \times\{0\},\end{aligned}\right.by proving that, for given {\delta\in(0,1)}, there exists {\varepsilon>0} depending on δ and the structural data such that\lvert\nabla u_{0}\rvert^{p+\varepsilon}\in L^{1}_{\operatorname{loc}}(\Omega)% \quad\text{and}\quad\lvert F\rvert^{p+\varepsilon},\lvert f\rvert^{(\frac{% \delta p(n+2)}{n})^{\prime}+\varepsilon}\in L^{1}(0,T;L^{1}_{\operatorname{loc% }}(\Omega))\implies\lvert\nabla u\rvert^{p+\varepsilon}\in L^{1}(0,T;L^{1}_{% \operatorname{loc}}(\Omega)).Our regularity results complement established higher regularity theories near the initial boundary for such a nonhomogeneous problem with {f\not\equiv 0} and we provide an optimal regularity theory in the literature.

scholarly journals Higher integrability for doubly nonlinear parabolic systems

2020 ◽  
Vol 143 ◽  
pp. 31-72 ◽  
Author(s):  
Verena Bögelein ◽  
Frank Duzaar ◽  
Juha Kinnunen ◽  
Christoph Scheven
Keyword(s):  
Parabolic Systems ◽  
Nonlinear Parabolic Systems ◽  
Higher Integrability ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear

Regularity for subquadratic parabolic systems: higher integrability and dimension estimates

2010 ◽  
Vol 140 (6) ◽  
pp. 1269-1308 ◽  
Author(s):  
Christoph Scheven
Keyword(s):  
Structure Function ◽  
Polynomial Growth ◽  
Time Derivative ◽  
Parabolic Systems ◽  
Spatial Gradient ◽  
Higher Integrability ◽  
Regularity Properties ◽  
Growth Properties ◽  
Spatial Derivatives ◽  
Image Position

We consider weak solutions of parabolic systems of the typewhere the structure function b is differentiable with respect to x and satisfies standard ellipticity and growth properties with polynomial growth rate p ∊ (2n/(n + 2), 2). We investigate regularity properties of the solution, including the existence of second-order spatial derivatives, the existence of the time derivative and the higher integrability of the spatial gradient. As an application, we derive dimension estimates for the singular set of solutions of homogeneous parabolic systems. More precisely, we establish the boundprovided the structure function depends Höolder continuously on the space variable with Höolder exponent β ∊(0, 1].

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