TY - JOUR
T1 - A proof of the Cp′-regularity conjecture in the plane
AU - Araújo, Damião J.
AU - Teixeira, Eduardo V.
AU - Urbano, José Miguel
N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15
PY - 2017/8/20
Y1 - 2017/8/20
N2 - We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class Cp′=C1, [Formula presented] this regularity is optimal.
AB - We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class Cp′=C1, [Formula presented] this regularity is optimal.
UR - https://linkinghub.elsevier.com/retrieve/pii/S0001870816316814
UR - http://www.scopus.com/inward/record.url?scp=85021291481&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2017.06.027
DO - 10.1016/j.aim.2017.06.027
M3 - Article
SN - 0001-8708
VL - 316
SP - 541
EP - 553
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -