scholarly journals Note on time-regularity for weak solutions to parabolic systems of $p$-Laplace type

2021 ◽  
Vol 149 (4) ◽  
pp. 1677-1685
Author(s):  
Simon Bortz ◽  
Moritz Egert ◽  
Olli Saari
Keyword(s):  
Weak Solutions ◽  
Parabolic Systems ◽  
Laplace Type

scholarly journals Very weak solutions of parabolic systems of p-Laplacian type

2002 ◽  
Vol 40 (1) ◽  
pp. 105-132 ◽  
Author(s):  
Juha Kinnunen ◽  
John L. Lewis
Keyword(s):  
Weak Solutions ◽  
Parabolic Systems ◽  
Very Weak Solutions

Regularity of weak solutions to linear and quasilinear parabolic systems of non-divergence type with non-smooth in time principal matrix: A(t)-caloric method

2017 ◽  
Vol 29 (5) ◽  
pp. 1039-1064 ◽  
Author(s):  
Arina A. Arkhipova ◽  
Jana Stará
Keyword(s):  
Approximation Method ◽  
Weak Solutions ◽  
Parabolic Systems ◽  
John 1 ◽  
Quasilinear Parabolic Systems ◽  
Regularity Of Weak Solutions ◽  
Divergence Type ◽  
Quasilinear Parabolic

AbstractWe prove a modification of the so-called A(t)-caloric lemma stated in our earlier work with O. John [1] to study regularity of weak solutions to parabolic systems of non-divergence type with non-smooth in time principal matrices. As an application, we prove smoothness results in Morrey and Campanato spaces for linear parabolic systems of non-divergence type by the A(t)-caloric approximation method.

scholarly journals Lp Estimates for Weak Solutions to Nonlinear Degenerate Parabolic Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Na Wei ◽  
Xiangyu Ge ◽  
Yonghong Wu ◽  
Leina Zhao
Keyword(s):  
Weak Solutions ◽  
Vector Fields ◽  
Parabolic Systems ◽  
Growth Conditions ◽  
Lp Estimates ◽  
Reverse Hölder Inequalities ◽  
Degenerate Parabolic Systems ◽  
Degenerate Parabolic ◽  
Reverse Hölder ◽  
Nonlinear Degenerate

This paper is devoted to the Lp estimates for weak solutions to nonlinear degenerate parabolic systems related to Hörmander’s vector fields. The reverse Hölder inequalities for degenerate parabolic system under the controllable growth conditions and natural growth conditions are established, respectively, and an important multiplicative inequality is proved; finally, we obtain the Lp estimates for the weak solutions by combining the results of Gianazza and the Caccioppoli inequality.

scholarly journals Infinitely many solutions for equations of p(x)-Laplace type with the nonlinear Neumann boundary condition

2017 ◽  
Vol 148 (1) ◽  
pp. 1-31 ◽  
Author(s):  
Eun Bee Choi ◽  
Jae-Myoung Kim ◽  
Yun-Ho Kim
Keyword(s):  
Weak Solutions ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Infinitely Many Solutions ◽  
Fountain Theorem ◽  
Neumann Problems ◽  
Neumann Boundary Value Problem ◽  
Cerami Condition ◽  
Image Position ◽  
Laplace Type

We investigate the following nonlinear Neumann boundary-value problem with associated p(x)-Laplace-type operatorwhere the function φ(x, v) is of type |v|p(x)−2v with continuous function p: → (1,∞) and both f : Ω × ℝ → ℝ and g : ∂Ω × ℝ → ℝ satisfy a Carathéodory condition. We first show the existence of infinitely many weak solutions for the Neumann problems using the Fountain theorem with the Cerami condition but without the Ambrosetti and Rabinowitz condition. Next, we give a result on the existence of a sequence of weak solutions for problem (P) converging to 0 in L∞-norm by employing De Giorgi's iteration and the localization method under suitable conditions.

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