arXiv subjects

Leandro G. Fernandes Jr

Publications and source records attributed to Leandro G. Fernandes Jr.

2 recordsLinked to original sources

arXiv2019

On existence and nonexistence of isoperimetric inequality with differents monomial weights

We consider the monomial weight $x^{A}=\vert x_{1}\vert^{a_{1}}\ldots\vert x_{N}\vert^{a_{N}}$, where $a_{i}$ is a nonnegative real number for each $i\in\{1,\ldots,N\}$, and we establish the existence and nonexistence of isoperimetric inequalities with different monomial weights. We study positive minimizers of $\int_{\partialΩ}x^{A}\mathcal{H}^{N-1}(x)$ among all smooth bounded sets $Ω$ in $\mathbb{R}^{N}$ with fixed Lebesgue measure with monomial weight $\int_Ωx^{B}dx$.

math.AP↗

arXiv2018

On a weighted Trudinger-Moser inequality in $\mathbb{R}^N$

We establish the Trudinger-Moser inequality on weighted Sobolev spaces in the whole space, and for a class of quasilinear elliptic operators in radial form of the type $\displaystyle Lu:=-r^{-θ}(r^α\vert u'(r)\vert^βu'(r))'$, where $θ, β\geq 0$ and $α>0$, are constants satisfying some existence conditions. It worth emphasizing that these operators generalize the $p$- Laplacian and $k$-Hessian operators in the radial case. Our results involve fractional dimensions, a new weighted Pólya-Szeg{ö} principle, and a boundness value for the optimal constant in a Gagliardo-Nirenberg type inequality.

math.AP↗