New gradient estimates for parabolic equations
Habermann J, Baroni P (2012)
Publication Type: Journal article
Publication year: 2012
Journal
Book Volume: 38
Pages Range: 855-914
Journal Issue: 3
Abstract
We prove sharp Lorentz-and Morrey-space estimates for the gradient of solutions u to nonlinear parabolic equations of the type ut div a(z;Du) = g; on T = (T; 0); where the vector field a is assumed to satisfy classical growth and ellipticity conditions and where the inhomogeneity g is only assumed to be integrable to some power > 1. In particular we investigate the case where stays below the exponent allowing for weak solutions u 2 L2(T; 0;W1;2( )). Our results extend { for p = 2 { the results for elliptic equations [48] to parabolic equations. © 2012 University of Houston.
Authors with CRIS profile
Involved external institutions
Italy (IT)How to cite
APA:
Habermann, J., & Baroni, P. (2012). New gradient estimates for parabolic equations. Houston Journal of Mathematics, 38(3), 855-914.
MLA:
Habermann, Jens, and Paolo Baroni. "New gradient estimates for parabolic equations." Houston Journal of Mathematics 38.3 (2012): 855-914.
BibTeX: Download