arXiv subjects

B. J. Bian

Publications and source records attributed to B. J. Bian.

2 recordsLinked to original sources

arXiv2005

The Second Order Estimate for Fully Nonlinear Uniformly Elliptic Equations without Concavity Assumption

Investigating for interior regularity of viscosity solutions to the fully nonlinear elliptic equation $$F(x,u,\triangledown u,\triangledown ^2 u)=0,$$ we establish the interior $C^{1+1}$ continuity under the assumptions that $F$ is uniformly elliptic, H$\ddot o$lder continuous and satisfies the natural structure conditions of fractional order, but without the concavity assumption of $F$. These assumptions are weaker and the result is stronger than that of Caffarelli and Wang[1], Chen[2].

math.AP↗

arXiv2001

Critical dynamics and universality of the random-bond Potts ferromagnet with tri-distributed quenched disorders

Critical behavior in short-time dynamics is investigated by a Monte Carlo study for the random-bond Potts ferromagnet with a trinary distribution of quenched disorders on two-dimensional triangular lattices. The dynamic scaling is verified and applied to estimate critical exponents $θ$, $z$ and $β/ν$ for several realizations of the trinary distribution. Our critical scaling analysis strongly indicates that the bond randomness influences the critical universality.

cond-mat.stat-mech↗