RT Journal Article
T1 A local regularity result for Neumann parabolic problems with nonsmooth data
A1 Martínez, A.
A1 Muñoz Sola, Rafael
A1 Vázquez Méndez, Miguel Ernesto
A1 Álvarez-Vázquez, L. J.
K1 Weak solution
K1 Transposition solution
K1 Convection–diffusion
K1 Measure data
K1 Neumann boundary condition
AB In this work we analyze the relations between two different concepts of solution of the Neumann problem for a second order parabolic equation: the usual notions of weak solution and those of transposition solution, which allow well-posedness of problems with measure data. We give a regularity result for the transposition solution and we prove that, under smoothness assumptions for the principal part of the operator, the local regularity of the transposition solution is the same as that of the usual weak solution. As an interesting particular case, we present a rigorous proof of local continuity of the solution for a convection–diffusion problem with pointwise source term.
PB Elsevier
SN 0019-3577
YR 2017
FD 2017
LK https://hdl.handle.net/10347/40791
UL https://hdl.handle.net/10347/40791
LA eng
NO Martínez, Muñoz-Sola, Vázquez-Méndez, & Alvarez-Vázquez. (2017). A local regularity result for Neumann parabolic problems with nonsmooth data. Indagationes Mathematicae, 28(2), 494-515. https://doi.org/10.1016/J.INDAG.2016.12.002
NO The research contained in this work was partially supported by Project MTM2015-65570-P of Ministerio de Economía y Competitividad (Spain) and FEDER. The authors also thank the interesting suggestions of the anonymous referee.
DS Minerva
RD 24 abr 2026