Giovanni Porru

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Laura Hartman

Boston University

Sebahattin Devecioglu

University of Firat

sean sayers

University of Kent

David Seamon

Kansas State University

Noe Cornago

University of the Basque Country, Euskal Herriko Unibertsitatea

Evangelos Bebetsos

Democritus University of Thrace

Kerstin P. Hofmann

German Archaeological Institute

Mariano Fernández-Enguita

Universidad Complutense de Madrid

Alan Garfinkel

California State University, Bakersfield

Muhammad A. Z. Mughal

King Fahd University of Petroleum and Minerals

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Papers by Giovanni Porru

Un risultato di regolarità per le soluzioni delle equazioni ellittiche degeneri del secondo ordine di tipo non variazionale

ANNALI DELL UNIVERSITA DI FERRARA

ABSTRACT

Boundary behaviour and integrability of large solutions to p-Laplace equations

Matemática Contemporânea, 2000

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Estimates for solutions to optimization problems on elliptic equations

We investigate a maximization problem involving the energy integral of the solutions to special e... more We investigate a maximization problem involving the energy integral of the solutions to special elliptic equations and find estimates concerning the optimal configurations. To prove our results we use a maximum principle for the P-function in case of weak solutions for general semilinear equations. Finally, we investigate the particular case of a dumbbell domain.

Minimization of the Principal Eigenvalue Under Neumann Boundary Conditions

Numerical Functional Analysis and Optimization, 2011

ABSTRACT We investigate the minimization of the principal eigenvalue of the Laplacian under Neuma... more ABSTRACT We investigate the minimization of the principal eigenvalue of the Laplacian under Neumann boundary conditions in case the weight has indefinite sign and varies in a class of rearrangements. Biologically, this minimization problem is motivated by the question of determining the most convenient spatial arrangement of favorable and unfavorable resources for a species to survive. The question may have practical importance in the context of reserve design.

On the Boundary Behaviour, Including Second Order Effects, of Solutions to Singular Elliptic Problems

Acta Mathematica Sinica, English Series, 2006

For γ ≥ 1 we consider the solution u = u(x) of the Dirichlet boundary value problem Δu + u -γ = 0... more For γ ≥ 1 we consider the solution u = u(x) of the Dirichlet boundary value problem Δu + u -γ = 0 in Ω, u = 0 on ∂Ω. For γ = 1 we find the estimate where p(r) ≈ r Ô 2 log(1/r) near r = 0, δ(x) denotes the distance from x to ∂Ω, 0 < < 1/2, and A(x) is a bounded function. For 1 < γ < 3 we find For γ = 3 we prove that u(x) = (2δ(x)) 1 2 1 + A(x)δ(x) log 1 δ(x) .

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Second-order estimates for boundary blowup solutions of special elliptic equations

DOAJ (DOAJ: Directory of Open Access Journals), 2006

We find a second-order approximation of the boundary blowup solution of the equation Δu = e u|u| ... more We find a second-order approximation of the boundary blowup solution of the equation Δu = e u|u| β-1 , with β > 0, in a bounded smooth domain Ω ⊂ R N . Furthermore, we consider the equation Δu = e u+e u . In both cases, we underline the effect of the geometry of the domain in the asymptotic expansion of the solutions near the boundary ∂Ω.

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Isoperimetric inequalities for -Hessian equations

Advances in Nonlinear Analysis, 2012

We consider the homogeneous Dirichlet problem for a special k-Hessian equation of sub-linear type... more We consider the homogeneous Dirichlet problem for a special k-Hessian equation of sub-linear type in a .k 1/-convex domain R n , 1 Ä k Ä n. We study the comparison between the solution of this problem and the (radial) solution of the corresponding problem in a ball having the same .k 1/-quermassintegral as. Next, we consider the eigenvalue problem for the k-Hessian equation and study a comparison between its principal eigenfunction and the principal eigenfunction of the corresponding problem in a ball having the same .k 1/-quermassintegral as. Symmetrization techniques and comparison principles are the main tools used to get these inequalities.

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Maximum principles for a class of nonlinear second order elliptic differential equations

arXiv (Cornell University), Apr 25, 1998

In this paper we investigate maximum principles for functionals defined on solutions to special p... more

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Estimates for solutions to nonlinear degenerate elliptic equations

CUBO, A Mathematical Journal, Sep 1, 2009

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On Monge-Ampère equations with nonlinear gradient terms – Infinite boundary value problems

Journal of Differential Equations, 2021

Abstract The paper investigates the existence, asymptotic boundary behavior and uniqueness of con... more

Placement of a source or a well for optimizing the energy integral

Electronic Journal of Differential Equations, 2018

This article concerns the maximization and minimization of the energy integral associated with so... more

$Research paper thumbnail of $\Theta$-Mappings and Quasiconformal Mappings in Normed Spaces$

$\Theta$-Mappings and Quasiconformal Mappings in Normed Spaces

Rendiconti del Seminario Matematico della Università di Padova, 1977

Symmetry of solutions to optimization problems related to partial differential equations

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2006

We investigate maxima and minima of some functionals associated with solutions to Dirichlet probl... more We investigate maxima and minima of some functionals associated with solutions to Dirichlet problems for elliptic equations. We prove existence results and, under suitable restrictions on the data, we show that any maximal configuration satisfies a special system of two equations. Next, we use the moving-plane method to find symmetry results for solutions of a system. We apply these results in our discussion of symmetry for the maximal configurations of the previous problem.

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Nonlinear elastic membranes involving the p-Laplacian operator

Electronic Journal of Differential …, 2006

This paper concerns an optimization problem related to the Poisson equation for the p-Laplace ope... more This paper concerns an optimization problem related to the Poisson equation for the p-Laplace operator, subject to homogeneous Dirichlet boundary conditions. Physically the Poisson equation models, for example, the deformation of a nonlinear elastic membrane which is fixed along the boundary, under load. A particular situation where the load is represented by a characteristic function is investigated.

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Second-order estimates for boundary blowup solutions of special elliptic equations

Boundary Value Problems, 2006

We find a second-order approximation of the boundary blowup solution of the equation Δu = e u|u| ... more We find a second-order approximation of the boundary blowup solution of the equation Δu = e u|u| β−1 , with β > 0, in a bounded smooth domain Ω ⊂ R N. Furthermore, we consider the equation Δu = e u+e u. In both cases, we underline the effect of the geometry of the domain in the asymptotic expansion of the solutions near the boundary ∂Ω.

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Maximization Problems for Second Order Elliptic Equations

Contemporary mathematics, 2021

We investigate the maxima in classes of rearrangements of some functionals associated with soluti... more

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Large solutions of quasilinear elliptic equations in the degenrate case

ABSTRACT

Asymptotic Behaviour and Convexity of Large Solutions to Nonlinear Equations

Inequalities and Applications, 1994

On the continuity of the minima of variational integrals in orlicz-sobolev spaces

Lecture Notes in Mathematics, 1985

ABSTRACT

Quasiconformal mappings in normed spaces

Lecture Notes in Mathematics, 1979

ABSTRACT

Un risultato di regolarità per le soluzioni delle equazioni ellittiche degeneri del secondo ordine di tipo non variazionale

ANNALI DELL UNIVERSITA DI FERRARA

ABSTRACT

Boundary behaviour and integrability of large solutions to p-Laplace equations

Matemática Contemporânea, 2000

Download

Estimates for solutions to optimization problems on elliptic equations

Minimization of the Principal Eigenvalue Under Neumann Boundary Conditions

Numerical Functional Analysis and Optimization, 2011

On the Boundary Behaviour, Including Second Order Effects, of Solutions to Singular Elliptic Problems

Acta Mathematica Sinica, English Series, 2006

Download

Second-order estimates for boundary blowup solutions of special elliptic equations

DOAJ (DOAJ: Directory of Open Access Journals), 2006

Download

Isoperimetric inequalities for -Hessian equations

Advances in Nonlinear Analysis, 2012

Download

Maximum principles for a class of nonlinear second order elliptic differential equations

arXiv (Cornell University), Apr 25, 1998

In this paper we investigate maximum principles for functionals defined on solutions to special p... more

Download

Estimates for solutions to nonlinear degenerate elliptic equations

CUBO, A Mathematical Journal, Sep 1, 2009

Download

On Monge-Ampère equations with nonlinear gradient terms – Infinite boundary value problems

Journal of Differential Equations, 2021

Abstract The paper investigates the existence, asymptotic boundary behavior and uniqueness of con... more

Placement of a source or a well for optimizing the energy integral

Electronic Journal of Differential Equations, 2018

This article concerns the maximization and minimization of the energy integral associated with so... more

$Research paper thumbnail of $\Theta$-Mappings and Quasiconformal Mappings in Normed Spaces$

$\Theta$-Mappings and Quasiconformal Mappings in Normed Spaces

Rendiconti del Seminario Matematico della Università di Padova, 1977

Symmetry of solutions to optimization problems related to partial differential equations

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2006

Download

Nonlinear elastic membranes involving the p-Laplacian operator

Electronic Journal of Differential …, 2006

Download

Second-order estimates for boundary blowup solutions of special elliptic equations

Boundary Value Problems, 2006

We find a second-order approximation of the boundary blowup solution of the equation Δu = e u|u| ... more We find a second-order approximation of the boundary blowup solution of the equation Δu = e u|u| β−1 , with β > 0, in a bounded smooth domain Ω ⊂ R N. Furthermore, we consider the equation Δu = e u+e u. In both cases, we underline the effect of the geometry of the domain in the asymptotic expansion of the solutions near the boundary ∂Ω.

Download

Maximization Problems for Second Order Elliptic Equations

Contemporary mathematics, 2021

We investigate the maxima in classes of rearrangements of some functionals associated with soluti... more

Download

Large solutions of quasilinear elliptic equations in the degenrate case

ABSTRACT

Asymptotic Behaviour and Convexity of Large Solutions to Nonlinear Equations

Inequalities and Applications, 1994

On the continuity of the minima of variational integrals in orlicz-sobolev spaces

Lecture Notes in Mathematics, 1985

ABSTRACT

Quasiconformal mappings in normed spaces

Lecture Notes in Mathematics, 1979

ABSTRACT

Giovanni Porru

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