Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Feo, Filomena"'
We prove the existence and uniqueness of weak solutions to a class of anisotropic elliptic equations with coefficients of convection term belonging to some suitable Marcinkiewicz spaces. Some useful a priori estimates and regularity results are also
Externí odkaz:
http://arxiv.org/abs/2307.13564
Autor:
Feo, Filomena, Takahashi, Futoshi
In this note, we characterize the equality case of the sharp $L^2$-Euclidean logarithmic Sobolev inequality with monomial weights, exploiting the idea by Bobkov and Ledoux \cite{Bob}. Our approach is new even in the unweighted case. Also, we show tha
Externí odkaz:
http://arxiv.org/abs/2208.03448
We study an anisotropic, possibly non-homogeneous version of the evolution $p$-Laplacian equation when fast diffusion holds in all directions. We develop the basic theory and prove symmetrization results from which we derive $L^1$ to $L^\infty$ estim
Externí odkaz:
http://arxiv.org/abs/2105.03981
In this paper we study a class of anisotropic equations with a lower order term whose coefficients lay in Marcinkiewicz spaces. We prove some regularity results for local solutions requiring any control on the norm of the coefficients.
Externí odkaz:
http://arxiv.org/abs/2011.13412
We prove the existence of self-similar fundamental solutions (SSF) of the anisotropic porous medium equation in the suitable fast diffusion range. Each of such SSF solutions is uniquely determined by its mass. We also obtain the asymptotic behaviour
Externí odkaz:
http://arxiv.org/abs/2007.00122
We derive some anisotropic Sobolev inequalities in $\mathbb{R}^{n}$ with a monomial weight in the general setting of rearrangement invariant spaces. Our starting point is to obtain an integral oscillation inequality in multiplicative form.
Externí odkaz:
http://arxiv.org/abs/1910.08996
Publikováno v:
In Nonlinear Analysis August 2023 233
Autor:
Feo, Filomena, Takahashi, Futoshi
We derive a sharp Logarithmic Sobolev inequality with monomial weights starting from a sharp Sobolev inequality with monomial weights. Several related inequalities such as Shannon type and Heisenberg's uncertain type are also derived. A characterizat
Externí odkaz:
http://arxiv.org/abs/1907.03439
Publikováno v:
Commun. Contemp. Math. 22, No. 3, Article ID 1950015, 32 p. (2020)
In this paper, the long-time asymptotic behaviours of nonlocal porous medium equations with absorption or convection are studied. In the parameter regimes when the nonlocal diffusion is dominant, the entropy method is adapted in this context to deriv
Externí odkaz:
http://arxiv.org/abs/1803.01697
Integral estimates for weak solutions to a class of Dirichlet problems for nonlinear, fully anisotropic, elliptic equations with a zero order term are obtained using symmetrization techniques.
Externí odkaz:
http://arxiv.org/abs/1711.10559