Second-order maximum principle preserving Strang’s splitting schemes for anisotropic fractional Allen-Cahn equations

2021 ◽  
Author(s):  
Hao Chen ◽  
Hai-Wei Sun
Keyword(s):  
Maximum Principle ◽  
Second Order ◽  
Splitting Schemes

scholarly journals A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

2021 ◽  
Author(s):  
Alessandro Goffi ◽  
Francesco Pediconi
Keyword(s):  
Maximum Principle ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Fully Nonlinear Equations ◽  
Nonlinear Operators ◽  
Fully Nonlinear ◽  
Second Order Equations ◽  
Curvature Type

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

Second order convex splitting schemes for periodic nonlocal Cahn–Hilliard and Allen–Cahn equations

2014 ◽  
Vol 277 ◽  
pp. 48-71 ◽  
Author(s):  
Zhen Guan ◽  
John S. Lowengrub ◽  
Cheng Wang ◽  
Steven M. Wise
Keyword(s):  
Second Order ◽  
Splitting Schemes ◽  
Convex Splitting
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