RT Journal Article
T1 Failure of the strong maximum principle for linear elliptic with singular convection of non-negative divergence
A1 Boccardo, L.
A1 Gómez Castro, David
A1 Díaz Díaz, Jesús Ildefonso
AB In this paper we study existence, uniqueness, and integrability of solutions to the Dirichlet problem −div(M(x)∇u)=−div(E(x)u)+f in a bounded domain of RN with N≥3. We are particularly interested in singular E with divE≥0. We start by recalling known existence results when |E|∈LN that do not rely on the sign of divE. Then, under the assumption that divE≥0 distributionally, we extend the existence theory to |E|∈L2. For the uniqueness, we prove a comparison principle in this setting. Lastly, we discuss the particular cases of E singular at one point as Ax/|x|2, or towards the boundary as divE∼dist(x,∂Ω)−2−α. In these cases the singularity of E leads to u vanishing to a certain order. In particular, this shows that the strong maximum principle fails in the presence of such singular drift terms E.
YR 2022
FD 2022-11-21
LK https://hdl.handle.net/20.500.14352/72748
UL https://hdl.handle.net/20.500.14352/72748
LA eng
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NO Unión Europea. Horizonte 2020
NO Ministerio de Ciencia e Innovación (MICINN)
NO Universidad Complutense de Madrid (UCM)
DS Docta Complutense
RD 3 may 2024