Nonlinear Analysis: Theory, Methods & Applications, 2009
This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the e... more This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet boundary conditions on the matter field, and either Dirichlet or Neumann boundary conditions on the electric potential.
In this paper we prove the existence of infinitely many radially symmetric standing waves in equi... more In this paper we prove the existence of infinitely many radially symmetric standing waves in equilibrium with their own electromagnetic field. The interaction is described by means of the minimal coupling rule; on the other hand the Lagrangian density for the electromagnetic field is the second order approximation of the Born-Infeld Lagrangian density.
We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary condi... more We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many standing waves.
We open the paper with introductory considerations describing the motivations of our long-term re... more We open the paper with introductory considerations describing the motivations of our long-term research plan targeting gravitomagnetism, illustrating the fluid-dynamics numerical test case selected for that purpose, that is, a perfect-gas sphere contained in a solid shell located in empty space sufficiently away from other masses, and defining the main objective of this study: the determination of the gravitofluid-static field required as initial field (t = 0) in forthcoming fluid-dynamics calculations. The determination of the gravitofluid-static field requires the solution of the isothermalsphere Lane-Emden equation. We do not follow the habitual approach of the literature based on the prescription of the central density as boundary condition; we impose the gravitational field at the solid-shell internal wall. As the discourse develops, we point out differences and similarities between the literature's and our approach. We show that the nondimensional formulation of the problem hinges on a unique physical characteristic number that we call gravitational number because it gauges the self-gravity effects on the gas' fluid statics. We illustrate and discuss numerical results; some peculiarities, such as gravitational-number upper bound and multiple solutions, lead us to investigate the thermodynamics of the physical system, particularly entropy and energy, and preliminarily explore whether or not thermodynamic-stability reasons could provide justification for either selection or exclusion of multiple solutions. We close the paper with a summary of the present study in which we draw conclusions and describe future work.
This paper deals with the Klein–Gordon–Maxwell system in a bounded spatial domain with a nonunifo... more This paper deals with the Klein–Gordon–Maxwell system in a bounded spatial domain with a nonuniform coupling. We discuss the existence of standing waves in equilibrium with a purely electrostatic field, assuming homogeneous Dirichlet boundary conditions on the matter field and nonhomogeneous Neumann boundary conditions on the electric potential. Under suitable conditions we prove existence and nonexistence results. Since the system is variational, we use Ljusternik–Schnirelmann theory.
ABSTRACT This paper deals with a model of solitary waves, in three space dimensions, which are ch... more ABSTRACT This paper deals with a model of solitary waves, in three space dimensions, which are characterized by a topological invariant called charge; these waves behave as relativistic particles. We study the interaction with an electromagnetic field. The Lagrangian density of the system is the sum of three terms: the first is that of the free soliton, the second is the classical Lagrangian density of an electromagnetic field, the third, which is due to the interaction, is chosen so that the electric charge coincides with the topological charge. We prove the existence of a static solution for every fixed value of the charge. The energy functional is strongly unbounded from above, as from below; after a reduction argument, the critical points are found by means of the Principle of Symmetric Criticality.
We study a Klein–Gordon–Maxwell system in a bounded spatial domain under Neumann boundary conditi... more We study a Klein–Gordon–Maxwell system in a bounded spatial domain under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many static solutions.
In this paper we study a class of Lorentz invariant nonlinear field equations in several space di... more In this paper we study a class of Lorentz invariant nonlinear field equations in several space dimensions. The main purpose is to obtain soliton-like solutions. These equations were essentially proposed by C. H. Derrick in a celebrated paper in 1964 as a model for elementary particles. However, an existence theory was not developed.
ABSTRACT We study a class of quasilinear elliptic equations suggested by C.H. Der-rick in 1964 as... more ABSTRACT We study a class of quasilinear elliptic equations suggested by C.H. Der-rick in 1964 as models for elementary particles. For scalar fields we prove some new nonexistence results. For vector-valued fields the situation is different as shown by recent results concerning the existence of solitary waves with a topological constraint.
ABSTRACT We study a class of field equations, in several space dimensions, which admits solitary ... more ABSTRACT We study a class of field equations, in several space dimensions, which admits solitary waves. The equation is a vector-valued version of a field equation proposed by Derrick in 1964 as model for elementary particles. We show the existence of infinitely many solutions with arbitrary topological charge.
Nonlinear Analysis: Theory, Methods & Applications, 2009
This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the e... more This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet boundary conditions on the matter field, and either Dirichlet or Neumann boundary conditions on the electric potential.
In this paper we prove the existence of infinitely many radially symmetric standing waves in equi... more In this paper we prove the existence of infinitely many radially symmetric standing waves in equilibrium with their own electromagnetic field. The interaction is described by means of the minimal coupling rule; on the other hand the Lagrangian density for the electromagnetic field is the second order approximation of the Born-Infeld Lagrangian density.
We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary condi... more We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many standing waves.
We open the paper with introductory considerations describing the motivations of our long-term re... more We open the paper with introductory considerations describing the motivations of our long-term research plan targeting gravitomagnetism, illustrating the fluid-dynamics numerical test case selected for that purpose, that is, a perfect-gas sphere contained in a solid shell located in empty space sufficiently away from other masses, and defining the main objective of this study: the determination of the gravitofluid-static field required as initial field (t = 0) in forthcoming fluid-dynamics calculations. The determination of the gravitofluid-static field requires the solution of the isothermalsphere Lane-Emden equation. We do not follow the habitual approach of the literature based on the prescription of the central density as boundary condition; we impose the gravitational field at the solid-shell internal wall. As the discourse develops, we point out differences and similarities between the literature's and our approach. We show that the nondimensional formulation of the problem hinges on a unique physical characteristic number that we call gravitational number because it gauges the self-gravity effects on the gas' fluid statics. We illustrate and discuss numerical results; some peculiarities, such as gravitational-number upper bound and multiple solutions, lead us to investigate the thermodynamics of the physical system, particularly entropy and energy, and preliminarily explore whether or not thermodynamic-stability reasons could provide justification for either selection or exclusion of multiple solutions. We close the paper with a summary of the present study in which we draw conclusions and describe future work.
This paper deals with the Klein–Gordon–Maxwell system in a bounded spatial domain with a nonunifo... more This paper deals with the Klein–Gordon–Maxwell system in a bounded spatial domain with a nonuniform coupling. We discuss the existence of standing waves in equilibrium with a purely electrostatic field, assuming homogeneous Dirichlet boundary conditions on the matter field and nonhomogeneous Neumann boundary conditions on the electric potential. Under suitable conditions we prove existence and nonexistence results. Since the system is variational, we use Ljusternik–Schnirelmann theory.
ABSTRACT This paper deals with a model of solitary waves, in three space dimensions, which are ch... more ABSTRACT This paper deals with a model of solitary waves, in three space dimensions, which are characterized by a topological invariant called charge; these waves behave as relativistic particles. We study the interaction with an electromagnetic field. The Lagrangian density of the system is the sum of three terms: the first is that of the free soliton, the second is the classical Lagrangian density of an electromagnetic field, the third, which is due to the interaction, is chosen so that the electric charge coincides with the topological charge. We prove the existence of a static solution for every fixed value of the charge. The energy functional is strongly unbounded from above, as from below; after a reduction argument, the critical points are found by means of the Principle of Symmetric Criticality.
We study a Klein–Gordon–Maxwell system in a bounded spatial domain under Neumann boundary conditi... more We study a Klein–Gordon–Maxwell system in a bounded spatial domain under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many static solutions.
In this paper we study a class of Lorentz invariant nonlinear field equations in several space di... more In this paper we study a class of Lorentz invariant nonlinear field equations in several space dimensions. The main purpose is to obtain soliton-like solutions. These equations were essentially proposed by C. H. Derrick in a celebrated paper in 1964 as a model for elementary particles. However, an existence theory was not developed.
ABSTRACT We study a class of quasilinear elliptic equations suggested by C.H. Der-rick in 1964 as... more ABSTRACT We study a class of quasilinear elliptic equations suggested by C.H. Der-rick in 1964 as models for elementary particles. For scalar fields we prove some new nonexistence results. For vector-valued fields the situation is different as shown by recent results concerning the existence of solitary waves with a topological constraint.
ABSTRACT We study a class of field equations, in several space dimensions, which admits solitary ... more ABSTRACT We study a class of field equations, in several space dimensions, which admits solitary waves. The equation is a vector-valued version of a field equation proposed by Derrick in 1964 as model for elementary particles. We show the existence of infinitely many solutions with arbitrary topological charge.
Uploads
Papers by Lorenzo Pisani