scholarly journals Hölder regularity and uniqueness theorem on weak solutions to the degenerate Keller–Segel system

2016 ◽  
Vol 138 ◽  
pp. 229-252 ◽  
Author(s):  
Sunghoon Kim ◽  
Ki-Ahm Lee
Keyword(s):  
Uniqueness Theorem ◽  
Weak Solutions ◽  
Hölder Regularity ◽  
Holder Regularity

scholarly journals Hölder regularity for degenerate parabolic equations with variable exponents

2022 ◽  
Vol 40 ◽  
pp. 1-19
Author(s):  
Hamid EL Bahja
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Hölder Regularity ◽  
Variable Exponents ◽  
Young’S Inequality ◽  
Scaling Method ◽  
Degenerate Parabolic ◽  
Young's Inequality ◽  
Holder Regularity

In this paper, we discuss a class of degenerate parabolic equations with variable exponents. By  using the Steklov average and Young's inequality, we establish energy and logarithmicestimates for solutions to these equations. Then based on the intrinsic scaling method, we provethat local weak solutions are locally continuous.

scholarly journals Hölder continuity of singular parabolic equations with variable nonlinearity

2020 ◽  
Vol 28 (3) ◽  
pp. 51-82
Author(s):  
Hamid El Bahja
Keyword(s):  
Iterative Method ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Hölder Continuity ◽  
Regularity Result ◽  
Hölder Regularity ◽  
Variable Exponents ◽  
Holder Continuity ◽  
Singular Parabolic Equations ◽  
Holder Regularity

AbstractIn this paper we obtain the local Hölder regularity of the weak solutions for singular parabolic equations with variable exponents. The proof is based on DiBenedetto’s technique called intrinsic scaling; by choosing an appropriate geometry one can deduce energy and logarithmic estimates from which one can implement an iterative method to obtain the regularity result.

Frequency and Energy Levels

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Weak Solutions ◽  
Energy Levels ◽  
Integration Scheme ◽  
Hölder Regularity ◽  
Reynolds Equations ◽  
Integration Procedure ◽  
Convex Integration ◽  
Interaction Term ◽  
Holder Regularity ◽  
Transport Term

This chapter shows how to measure the Hölder regularity of the weak solutions that are constructed when the scheme is executed more carefully. For this aspect of the convex integration scheme, a notion of frequency energy levels is introduced. This notion is meant to accurately record the bounds which apply to the (v, p, R) coming from the previous stage of the construction. The chapter presents an example of a candidate definition for frequency and energy levels. Based on this definition, the effect of one iteration of the convex integration procedure can be summarized in a single lemma, which states that there is a solution to the Euler-Reynolds equations with new frequency and energy levels. The chapter also considers the High–Low Interaction term and the Transport term.

scholarly journals Local Hölder Regularity of Weak Solutions for Singular Parabolic Systems of p-Laplacian Type

CAUCHY ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 136-141
Author(s):  
Khoirunisa Khoirunisa ◽  
Corina Karim ◽  
M. Muslikh
Keyword(s):  
Weak Solutions ◽  
Poincaré Inequality ◽  
Parabolic Systems ◽  
Hölder Regularity ◽  
Poincare Inequality ◽  
Holder Space ◽  
Hölder Space ◽  
Regularity Of Weak Solutions ◽  
Holder Regularity

In this paper, the Hölder regularity of weak solutions for singular parabolic systems of p-Laplacian type is investigated. By the Poincare inequality, we show that its weak solutions within Hölder space.

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