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Ariel Martin Salort

Bio: Ariel Martin Salort is an academic researcher from University of Buenos Aires. The author has contributed to research in topics: Sobolev space & Eigenvalues and eigenvectors. The author has an hindex of 12, co-authored 87 publications receiving 516 citations. Previous affiliations of Ariel Martin Salort include Facultad de Ciencias Exactas y Naturales & National Scientific and Technical Research Council.


Papers
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Journal ArticleDOI
TL;DR: In this article, the authors define the fractional order Orlicz-Sobolev spaces and prove their convergence to the classical ORCLS spaces when s ≥ 1 in the spirit of the celebrated result of Bourgain-Brezis-Mironescu.

92 citations

Journal ArticleDOI
TL;DR: In this article, the eigenvalues and minimizers of a fractional non-standard growth problem were studied and several properties on these quantities and their corresponding eigenfunctions were proved.

51 citations

Journal ArticleDOI
TL;DR: In this paper, a homogeneous fractional Sobolev space obtained by completion of the space of smooth test functions, with respect to a S-Sobolev-Slobodecki norm, is considered.
Abstract: We consider a homogeneous fractional Sobolev space obtained by completion of the space of smooth test functions, with respect to a Sobolev–Slobodeckiĭ norm. We compare it to the fractional Sobolev space obtained by the K-method in real interpolation theory. We show that the two spaces do not always coincide and give some sufficient conditions on the open sets for this to happen. We also highlight some unnatural behaviors of the interpolation space. The treatment is as self-contained as possible.

32 citations

Posted Content
TL;DR: In this article, the authors define the fractional order Orlicz-Sobolev spaces and prove its convergence to the classical Orlac-Sobs-Sorev spaces when the fraction fractional parameter $s\uparrow 1$ in the spirit of the celebrated result of Bourgain-Brezis-Mironescu.
Abstract: In this paper we define the fractional order Orlicz-Sobolev spaces, and prove its convergence to the classical Orlicz-Sobolev spaces when the fractional parameter $s\uparrow 1$ in the spirit of the celebrated result of Bourgain-Brezis-Mironescu. We then deduce some consequences such as $\Gamma-$convergence of the modulars and convergence of solutions for some fractional versions of the $\Delta_g$ operator as the fractional parameter $s\uparrow 1$.

30 citations

Journal ArticleDOI
TL;DR: In this article, the polarization technique was used to prove modular and norm Polya-Szego inequalities in general fractional Orlicz-Sobolev spaces.
Abstract: In this article, we prove modular and norm Polya–Szego inequalities in general fractional Orlicz–Sobolev spaces by using the polarization technique. We introduce a general framework which includes ...

26 citations


Cited by
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Journal ArticleDOI
TL;DR: Kaufmann et al. as discussed by the authors presented the work of the Centro de Investigacion y Estudios de Matematica (CESM) at the Universidad Nacional de Cordoba.
Abstract: Fil: Kaufmann, Uriel. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Cordoba. Centro de Investigacion y Estudios de Matematica. Universidad Nacional de Cordoba. Centro de Investigacion y Estudios de Matematica; Argentina

130 citations

01 Jan 2016
TL;DR: The optimal shape design for elliptic systems is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.
Abstract: Thank you for reading optimal shape design for elliptic systems. Maybe you have knowledge that, people have search hundreds times for their favorite books like this optimal shape design for elliptic systems, but end up in infectious downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they juggled with some infectious bugs inside their laptop. optimal shape design for elliptic systems is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the optimal shape design for elliptic systems is universally compatible with any devices to read.

116 citations

Book ChapterDOI
01 Jan 2007
TL;DR: In this paper, the basic idea behind the minimax method is to find a critical value of a functional ϕ ∈ C1 (X, ℝ) as a minimax (or maximin) value c ∈ ϕ of ϕ over a suitable class A of subsets of X.
Abstract: Roughly speaking, the basic idea behind the so-called minimax method is the following: Find a critical value of a functional ϕ ∈ C1 (X, ℝ) as a minimax (or maximin) value c ∈ ℝ of ϕ over a suitable class A of subsets of X: $$ c = \mathop {\inf }\limits_{A \in \mathcal{A}} \mathop {\sup }\limits_{u \in A} \phi \left( u \right). $$

73 citations

01 Jan 1999

60 citations