Abstract
AbstractWe provide a higher integrability result for the gradient of positive solutions to Trudinger’s equation (also known as the doubly non-linear equation) for the range $$p\in [2,\infty )$$
p
∈
[
2
,
∞
)
. The estimate is achieved by refining a construction of intrinsic cylinders from the vectorial setting by incorporating estimates that are only available in the scalar case.
Funder
DFG
Univerzita Karlova v Praze
Grantová Agentura Çeské Republiky
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference26 articles.
1. Bögelein, V., Duzaar, F., Kinnunen, J., Scheven, C.: Higher integrability for doubly nonlinear parabolic systems. J. Math. Pures Appl. 9(143), 31–72 (2020)
2. Bögelein, V., Duzaar, F., Korte, R., Scheven, C.: The higher integrability of weak solutions of porous medium systems. Adv. Nonlinear Anal. 8, 1004–1034 (2019)
3. Boyarskiĭ, B.V.: Generalized solutions of a system of differential equations of first order and of elliptic type with discontinuous coefficients. Math. Sb. N.S. 43(85), 451–503 (1957)
4. DiBenedetto, E.: Degenerate Parabolic Equations. Springer, New York (1993)
5. DiBenedetto, E., Friedman, A.: Hölder estimates for non-linear degenerate parabolic systems. J. Reine Angew. Math. 357, 1–22 (1985)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Higher integrability for singular doubly nonlinear systems;Annali di Matematica Pura ed Applicata (1923 -);2024-04-09
2. Higher integrability for doubly nonlinear parabolic systems;Partial Differential Equations and Applications;2022-10-18