6533b7cffe1ef96bd1258e99
RESEARCH PRODUCT
On the second-order regularity of solutions to the parabolic p-Laplace equation
Yawen FengMikko ParviainenSaara Sarsasubject
osittaisdifferentiaaliyhtälötp-parabolic functionstime derivativeSobolev regularityMathematics::Analysis of PDEsfundamental inequalityWeak solutionsMathematics (miscellaneous)Fundamental inequalityweak solutionsGRADIENT111 MathematicsTime derivativeEQUIVALENCEdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-02-26 |