Abstract
AbstractIn this paper, we study the second-order Sobolev regularity of solutions to the parabolic p-Laplace equation. For any p-parabolic function u, we show that $$D(\left| Du\right| ^{\frac{p-2+s}{2}}Du)$$
D
(
D
u
p
-
2
+
s
2
D
u
)
exists as a function and belongs to $$L^{2}_{\text {loc}}$$
L
loc
2
with $$s>-1$$
s
>
-
1
and $$1<p<\infty $$
1
<
p
<
∞
. The range of s is sharp.
Funder
China Scholarship Council
Academy of Finland
Academy of Finland, the Centre of Excellence in Analysis and Dynamics Research
Publisher
Springer Science and Business Media LLC
Subject
Mathematics (miscellaneous)
Reference24 articles.
1. A. Attouchi and E. Ruosteenoja. Remarks on regularity for $$p$$-Laplacian type equations in non-divergence form. J. Differential Equations, 265(5):1922–1961, 2018.
2. V. Bögelein, F. Duzaar, and G. Mingione. The regularity of general parabolic systems with degenerate diffusion. Mem. Amer. Math. Soc., 221(1041):vi+143, 2013.
3. B. Bojarski and T. Iwaniec. $$p$$-harmonic equation and quasiregular mappings. Partial differential equations (Warsaw, 1984), Banach Center Publ., 19, PWN, Warsaw: 25–38, 1987.
4. Y. Chen. Hölder continuity of the gradient of the solutions of certain degenerate parabolic equations. Chinese Ann. Math. Ser. B, 8(3):343–356, 1987. A Chinese summary appears in Chinese Ann. Math. Ser. A 8 (1987), no. 3, 534.
5. A. Cianchi and V.G. Maz’ya. Second-order regularity for parabolic $$p$$-Laplace problems. J. Geom. Anal., 30(2):1565–1583, 2020.
Cited by
1 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