A formula of the regularized trace for power of the laplace operator with potential on a tetrahedron in case of the dirichlet boundary problem

10.12737/5215 ◽  
2014 ◽  
Vol 2 (4) ◽  
pp. 464-467
Author(s):  
N. Tomin ◽  
I. Tomina
Keyword(s):  
Boundary Problem ◽  
Laplace Operator ◽  
Dirichlet Boundary ◽  
Regularized Trace ◽  
The Laplace Operator ◽  
Dirichlet Boundary Problem

scholarly journals On a Differential Inclusion Involving Dirichlet–Laplace Operators of Fractional Orders

2020 ◽  
Vol 43 (6) ◽  
pp. 4089-4106
Author(s):  
Rafał Kamocki
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusion ◽  
Laplace Operator ◽  
Spectral Decomposition ◽  
Convex Analysis ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Fenchel Transform ◽  
The Laplace Operator ◽  
Fractional Orders

Abstract In this paper, we investigate a nonlinear differential inclusion with Dirichlet boundary conditions containing a weak Laplace operator of fractional orders (defined via the spectral decomposition of the Laplace operator $$-{\varDelta }$$ - Δ under Dirichlet boundary conditions). Using variational methods, we characterize solutions of such a problem. Our approach is based on tools from convex analysis (properties of a Legendre–Fenchel transform).

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