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pro vyhledávání: '"Soudsky, Filip"'
Autor:
Soudský, Filip
In this thesis we shall provide the reader with results in the field of classical Lorentz spaces. These spaces have been studied since the 50's and have many applications in partial differential equations and interpolation theory. This work includes
Externí odkaz:
http://www.nusl.cz/ntk/nusl-349363
Autor:
Soudský, Filip
In this thesis we focus on generalized Gamma spaces GΓ(p, m, v) and classify some of their intrinsic properties. In an article called Relative Re- arrangement Methods for Estimating Dual Norm (for details see references), the authors attempted to ch
Externí odkaz:
http://www.nusl.cz/ntk/nusl-313763
We prove a new type of pointwise estimate of the Kalamajska-Mazya-Shaposhnikova type, where sparse averaging operators replace the maximal operator. It allows us to extend the Gagliardo-Nirenberg interpolation inequality to all rearrangement invarian
Externí odkaz:
http://arxiv.org/abs/2403.07096
Autor:
Roskovec, Tomáš G., Soudský, Filip
The weak lower semicontinuity of the functional $$ F(u)=\int_{\Omega}f(x,u,\nabla u)\, dx$$ is a classical topic that was studied thoroughly. It was shown that if the function $f$ is continuous and convex in the last variable, the functional is seque
Externí odkaz:
http://arxiv.org/abs/2302.03489
We prove optimality of the Gagliardo-Nirenberg inequality $$ \|\nabla u\|_{X}\lesssim\|\nabla^2 u\|_Y^{1/2}\|u\|_Z^{1/2}, $$ where $Y, Z$ are rearrangement invariant Banach function spaces and $X=Y^{1/2}Z^{1/2}$ is the Calder\'on--Lozanovskii space.
Externí odkaz:
http://arxiv.org/abs/2112.11570
Autor:
Campbell, Daniel, Soudský, Filip
Given any $f$ a locally finitely piecewise affine homeomorphism of $\Omega \subset \rn$ onto $\Delta \subset \rn$ in $W^{1,p}$, $1\leq p < \infty$ and any $\epsilon >0$ we construct a smooth injective map $\tilde{f}$ such that $\|f-\tilde{f}\|_{W^{1,
Externí odkaz:
http://arxiv.org/abs/2102.06450
Let $\Omega\subseteq\mathcal{R}^2$ be a domain, let $X$ be a rearrangement invariant space and let $f\in W^{1}X(\Omega,\mathcal{R}^2)$ be a homeomorphism between $\Omega$ and $f(\Omega)$. Then there exists a sequence of diffeomorphisms $f_k$ convergi
Externí odkaz:
http://arxiv.org/abs/2005.04998
We study the regularity properties of the inverse of a bilipschitz mapping $f$ belonging $W^m X_{\text{loc}}$, where $X$ is an arbitrary Banach function space. Namely, we prove that the inverse mapping $f^{-1}$ is also in $W^m X_{\text{loc}}$. Furthe
Externí odkaz:
http://arxiv.org/abs/1901.01878
The classical Gagliardo-Nirenberg interpolation inequality is a well-known estimate which gives, in particular, an estimate for the Lebesgue norm of intermediate derivatives of functions in Sobolev spaces. We present an extension of this estimate int
Externí odkaz:
http://arxiv.org/abs/1812.04295
A carefully written Nirenberg's proof of the well known Gagliardo-Nirenberg interpolation inequality for intermediate derivatives in $\mathbb{R}^n$ seems, surprisingly, to be missing in literature. In our paper we shall first introduce this fundament
Externí odkaz:
http://arxiv.org/abs/1812.04281