arXiv subjects

Sonia Acinas

Publications and source records attributed to Sonia Acinas.

4 recordsLinked to original sources

arXiv2024

Extension of the Best Polynomial Operator in Generalized Orlicz spaces

In this paper, we consider the best multivalued polynomial approximation operator for functions in an Orlicz Space $L^{\varphi}(\Omega)$. We obtain its characterization involving $\psi^-$ and $\psi^+$, which are the left and right derivatives functions of $\varphi$. And then, we extend the operator to $L^{\psi^+}(\Omega)$. We also get pointwise convergence of this extension, where the Calder\'on-Zygmund class $t_m^p (x)$ adapted to $L^{\psi^+}(\Omega)$ plays an important role.

math.CA↗

arXiv2018

Clarke duality for Hamiltonian systems with nonstandard growth

We consider the existence of periodic solutions to Hamiltonian Systems with growth conditions involving G-function. We introduce the notion of symplectic G-function and provide relation for the growth of Hamiltonian in terms of certain constant $C_G$ associated to symplectic G-function $G$. We discuss an optimality of this constant for some special cases. We also provide an applications to the $Φ$-laplacian type systems.

math.CA↗

arXiv2017

Periodic solutions of Euler-Lagrange equations in an anisotropic Orlicz-Sobolev space setting

In this paper we consider the problem of finding periodic solutions of certain Euler-Lagrange equations, which include, among others, equations involving the $p$-Laplace and, more generality, the $(p,q)$-Laplace operator. We employ the direct method of the calculus of variations in the framework of anisotropic Orlicz-Sobolev spaces. These spaces appear to be useful in formulating a unified theory of existence for the type of problem considered.

math.CA↗

arXiv2017

Periodic solutions of Euler-Lagrange equations with sublinear pontentials in an Orlicz-Sobolev space setting

In this paper, we obtain existence results of periodic solutions of hamiltonian systems in the Orlicz-Sobolev space $W^1L^Φ([0,T])$. We employ the direct method of calculus of variations and we consider a potential function $F$ satisfying the inequality $|\nabla F(t,x)|\leq b_1(t) Φ_0'(|x|)+b_2(t)$, with $b_1, b_2\in L^1$ and certain $N$-functions $Φ_0$.

math.CA↗