Self-Adjointness: Part 1. The Kato Inequality

1996 ◽  
pp. 77-87
Author(s):  
P. D. Hislop ◽  
I. M. Sigal
Keyword(s):  
Kato Inequality

Heat equation with a singular potential on the boundary and the Kato inequality

2012 ◽  
Vol 118 (1) ◽  
pp. 161-176 ◽  
Author(s):  
Kazuhiro Ishige ◽  
Michinori Ishiwata
Keyword(s):  
Heat Equation ◽  
Singular Potential ◽  
Kato Inequality

scholarly journals Heinz–Kato inequality in Banach spaces

2019 ◽  
Vol 28 (3) ◽  
pp. 841-846
Author(s):  
Nikolaos Roidos
Keyword(s):  
Banach Spaces ◽  
Kato Inequality

Boundedness of solutions to Ginzburg–Landau fractional Laplacian equation

2016 ◽  
Vol 27 (05) ◽  
pp. 1650048 ◽  
Author(s):  
Li Ma
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fractional Laplacian ◽  
Boundedness Of Solutions ◽  
Ginzburg Landau ◽  
Fractional Schrödinger Equation ◽  
Laplacian Equation ◽  
Kato Inequality ◽  
Fractional Schrodinger Equation

In this paper, we give the boundedness of solutions to Ginzburg–Landau fractional Laplacian equation, which extends the Herve–Herve theorem into the nonlinear fractional Laplacian equation. We follow Brezis’ idea to use the Kato inequality. A related linear fractional Schrödinger equation is also studied.

Stability of the two-dimensional Brown–Ravenhall operator

2002 ◽  
Vol 132 (5) ◽  
pp. 1133-1144 ◽  
Author(s):  
A. Bouzouina
Keyword(s):  
Critical Value ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Kato Inequality

We prove that the two-dimensional Brown–Ravenhall operator is bounded from below when the coupling constant is below a specified critical value—a property also referred to as stability. As a consequence, the operator is then self-adjoint. The proof is based on the strategy followed by Evans et al. and Lieb and Yau, with some relevant changes characteristic of the dimension. Our analysis also yields a sharp Kato inequality.

scholarly journals The Hijazi Inequalities on Complete RiemannianSpincManifolds

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Roger Nakad
Keyword(s):  
Dirac Operator ◽  
Essential Spectrum ◽  
Finite Volume ◽  
Energy Momentum Tensor ◽  
Type Inequality ◽  
Momentum Tensor ◽  
Kato Inequality ◽  
Additional Assumptions

We extend the Hijazi type inequality, involving the energy-momentum tensor, to the eigenvalues of the Dirac operator on complete Riemannian Spincmanifolds without boundary and of finite volume. Under some additional assumptions, using the refined Kato inequality, we prove the Hijazi type inequality for elements of the essential spectrum. The limiting cases are also studied.

scholarly journals On the constants in a Kato inequality for the Euler and Navier-Stokes equations

2012 ◽  
Vol 11 (2) ◽  
pp. 557-586 ◽  
Author(s):  
Carlo Morosi ◽  
◽  
Livio Pizzocchero ◽  
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Kato Inequality

Stability of the two-dimensional Brown–Ravenhall operator

2002 ◽  
Vol 132 (5) ◽  
pp. 1133-1144 ◽  
Author(s):  
A. Bouzouina
Keyword(s):  
Critical Value ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Kato Inequality

We prove that the two-dimensional Brown–Ravenhall operator is bounded from below when the coupling constant is below a specified critical value—a property also referred to as stability. As a consequence, the operator is then self-adjoint. The proof is based on the strategy followed by Evans et al. and Lieb and Yau, with some relevant changes characteristic of the dimension. Our analysis also yields a sharp Kato inequality.

scholarly journals Uniqueness and comparison principles for semilinear equations and inequalities in Carnot groups

2018 ◽  
Vol 7 (3) ◽  
pp. 313-325 ◽  
Author(s):  
Lorenzo D’Ambrosio ◽  
Enzo Mitidieri
Keyword(s):  
Carnot Groups ◽  
Liouville Theorems ◽  
Comparison Principles ◽  
Semilinear Equations ◽  
Distributional Solutions ◽  
Kato Inequality

AbstractVariants of the Kato inequality are proved for distributional solutions of semilinear equations and inequalities on Carnot groups. Various applications to uniqueness, comparison of solutions and Liouville theorems are presented.

Point interactions on bounded domains

1994 ◽  
Vol 124 (5) ◽  
pp. 917-926 ◽  
Author(s):  
Wim Caspers ◽  
Guido Sweers
Keyword(s):  
Boundary Condition ◽  
Analytic Semigroup ◽  
Dirichlet Boundary ◽  
Dirac Measure ◽  
Laplacian Operator ◽  
Bounded Domains ◽  
Evolutionary System ◽  
Point Interactions ◽  
Nirenberg Inequality ◽  
Kato Inequality

The Laplacian operator Δ on a bounded domain Ω in ℝn containing 0, with Dirichlet boundary condition, is perturbed by a pseudopotential δ, the Dirac measure at 0. Such a perturbation will be defined in Lp(ℝ) for n = 2, 1 <lt; p < ∞, and for n = 3, < p < 3, and is shown to be the generator of an analytic semigroup. Thus solutions of the corresponding evolutionary system are well defined. The necessary estimates involve the Gagliardo– Nirenberg inequality and the Kato inequality.

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