Search results for "RICH"

Existence of non-zero solutions for a Dirichlet problem driven by (p(x),q(x)-Laplacian

2021

The paper focuses on a Dirichlet problem driven by the (Formula presented.) -Laplacian. The existence of at least two non-zero solutions under suitable conditions on the nonlinear term is established. The approach is based on variational methods.

Symmetrization for singular semilinear elliptic equations

2012

In this paper, we prove some comparison results for the solution to a Dirichlet problem associated with a singular elliptic equation and we study how the summability of such a solution varies depending on the summability of the datum f. © 2012 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.

Existence and comparison results for a singular semilinear elliptic equation with a lower order term

2014

This paper deals with the homogeneous Dirichlet problem for a singular semilinear elliptic equation with a first order term. When the datum is bounded we prove an existence result and we show that any solution can be compared with the solution to a suitable symmetrized problem.

On Noncoercive (p, q)-Equations

2021

We consider a nonlinear Dirichlet problem driven by a (p, q)-Laplace differential operator (1 < q < p). The reaction is (p - 1)-linear near +/-infinity and the problem is noncoercive. Using variational tools and truncation and comparison techniques together with critical groups, we produce five nontrivial smooth solutions all with sign information and ordered. In the particular case when q = 2, we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.

Nonlinear Diffusion in Transparent Media

2021

Abstract We consider a prototypical nonlinear parabolic equation whose flux has three distinguished features: it is nonlinear with respect to both the unknown and its gradient, it is homogeneous, and it depends only on the direction of the gradient. For such equation, we obtain existence and uniqueness of entropy solutions to the Dirichlet problem, the homogeneous Neumann problem, and the Cauchy problem. Qualitative properties of solutions, such as finite speed of propagation and the occurrence of waiting-time phenomena, with sharp bounds, are shown. We also discuss the formation of jump discontinuities both at the boundary of the solutions’ support and in the bulk.

Multiple solutions for parametric double phase Dirichlet problems

2020

We consider a parametric double phase Dirichlet problem. Using variational tools together with suitable truncation and comparison techniques, we show that for all parametric values [Formula: see text] the problem has at least three nontrivial solutions, two of which have constant sign. Also, we identify the critical parameter [Formula: see text] precisely in terms of the spectrum of the [Formula: see text]-Laplacian.

Uniform rectifiability implies Varopoulos extensions

2020

We construct extensions of Varopolous type for functions $f \in \text{BMO}(E)$, for any uniformly rectifiable set $E$ of codimension one. More precisely, let $\Omega \subset \mathbb{R}^{n+1}$ be an open set satisfying the corkscrew condition, with an $n$-dimensional uniformly rectifiable boundary $\partial \Omega$, and let $\sigma := \mathcal{H}^n\lfloor_{\partial \Omega}$ denote the surface measure on $\partial \Omega$. We show that if $f \in \text{BMO}(\partial \Omega,d\sigma)$ with compact support on $\partial \Omega$, then there exists a smooth function $V$ in $\Omega$ such that $|\nabla V(Y)| \, dY$ is a Carleson measure with Carleson norm controlled by the BMO norm of $f$, and such th…

Finite element approximations of the wave equation with Dirichlet boundary data defined on a bounded domain in R2

2006

Three solutions to mixed boundary value problem driven by p(z)-Laplace operator

2021

We prove the existence of at least three weak solutions to a mixed Dirichlet–Neumann boundary value problem for equations driven by the p(z)-Laplace operator in the principal part. Our approach is variational and use three critical points theorems.

Quattro mega inceneritori e quattro mega discariche

2014

Lo smaltimento in discarica, così come l’incenerimento, sono nocivi e insostenibili ambientalmente, oltre che costosi e dissipano le materie prime contenute nei rifiuti.