Minimizers of mass critical Hartree energy functionals in bounded domains

2018 ◽  
Vol 265 (10) ◽  
pp. 5177-5211 ◽  
Author(s):  
Yujin Guo ◽  
Yong Luo ◽  
Qi Zhang
Keyword(s):  
Bounded Domains ◽  
Energy Functionals ◽  
Hartree Energy

Energy Functionals and Complex Monge–Ampère Equations

2010 ◽  
Vol 9 (3) ◽  
pp. 463-476 ◽  
Author(s):  
Zuoliang Hou ◽  
Qi Li
Keyword(s):  
Boundary Conditions ◽  
Bounded Domains ◽  
Energy Functionals ◽  
Convergence Of Solutions ◽  
Monge Ampere

AbstractWe introduce certain energy functionals to complex Monge–Ampère equations over bounded domains with inhomogeneous boundary conditions, and use these functionals to show the convergence of solutions to certain parabolic Monge–Ampère equations.

Fractional abstract Cauchy problem on complex interpolation scales

2020 ◽  
Vol 23 (4) ◽  
pp. 1125-1140
Author(s):  
Andriy Lopushansky ◽  
Oleh Lopushansky ◽  
Anna Szpila
Keyword(s):  
Cauchy Problem ◽  
Time Derivative ◽  
Abstract Cauchy Problem ◽  
Initial Boundary ◽  
Sectorial Operator ◽  
Complex Interpolation ◽  
Bounded Domains ◽  
Initial Boundary Value Problems ◽  
Fractional Time Derivative ◽  
Initial Boundary Value

AbstractAn fractional abstract Cauchy problem generated by a sectorial operator is investigated. An inequality of coercivity type for its solution with respect to a complex interpolation scale generated by a sectorial operator with the same parameters is established. An application to differential parabolic initial-boundary value problems in bounded domains with a fractional time derivative is shown.

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