Abstract
AbstractIn this paper we establish a higher integrability result up to the boundary of weak solutions to doubly nonlinear parabolic systems. We show that the spatial gradient of a weak solution with vanishing lateral boundary values is integrable to a larger power than the natural power p, where the statement holds for parameters in the subquadratic case $$ \max \lbrace \frac{2n}{n+2}, 1 \rbrace < p \le 2$$
max
{
2
n
n
+
2
,
1
}
<
p
≤
2
.
Funder
FWF
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference30 articles.
1. Adimurthi, K., Byun, S.-S.: Boundary higher integrability for very weak solutions of quasilinear parabolic equations. J. Math. Pures Appl. 9(121), 244–285 (2019)
2. Bögelein, V.: Higher integrability for weak solutions of higher order degenerate parabolic systems. Ann. Acad. Sci. Fenn. 33, 387–412 (2008)
3. Bögelein, V., Duzaar, F., Gianazza, U.: Porous medium type equations with measure data and potential estimates. SIAM J. Math. Anal. 45, 3283–3330 (2013)
4. Bögelein, V., Duzaar, F., Kinnunen, J., Scheven, C.: Higher integrability for doubly nonlinear parabolic systems. Journal de Mathématiques Pures et Appliquées 143, 31–72 (2020)
5. 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)