Lukáš Malý
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View article: A Hybrid Sobolev Gradient Method for Learning NODEs
A Hybrid Sobolev Gradient Method for Learning NODEs Open
The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in ordinary differential equations is considered, with the typical application of finding weights of a neural ordinary differential equation (NO…
View article: A simple proof of reflexivity and separability of N^{1,p} Sobolev spaces
A simple proof of reflexivity and separability of N^{1,p} Sobolev spaces Open
We present an elementary proof of a well-known theorem of Cheeger which states that if a metric-measure space \(X\) supports a \(p\)-Poincaré inequality, then the \(N^{1,p}(X)\) Sobolev space is reflexive and separable whenever \(p\in (1,\…
View article: A simple proof of reflexivity and separability of $N^{1,p}$ Sobolev spaces
A simple proof of reflexivity and separability of $N^{1,p}$ Sobolev spaces Open
We present an elementary proof of a well-known theorem of Cheeger which states that if a metric-measure space $X$ supports a $p$-Poincaré inequality, then the $N^{1,p}(X)$ Sobolev space is reflexive and separable whenever $p\in (1,\infty)$…
View article: An Analog of the Neumann Problem for the 1-Laplace Equation in the Metric Setting: Existence, Boundary Regularity, and Stability
An Analog of the Neumann Problem for the 1-Laplace Equation in the Metric Setting: Existence, Boundary Regularity, and Stability Open
We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a Poincaré inequality. We show that solutions exist under ce…
View article: Domains in metric measure spaces with boundary of positive mean\n curvature, and the Dirichlet problem for functions of least gradient
Domains in metric measure spaces with boundary of positive mean\n curvature, and the Dirichlet problem for functions of least gradient Open
We study the geometry of domains in complete metric measure spaces equipped\nwith a doubling measure supporting a $1$-Poincar\\'e inequality. We propose a\nnotion of \\emph{domain with boundary of positive mean curvature} and prove\nthat, …
View article: Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient
Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient Open
We study the geometry of domains in complete metric measure spaces equipped with a doubling measure supporting a $1$-Poincaré inequality. We propose a notion of \emph{domain with boundary of positive mean curvature} and prove that, for suc…
View article: Trace and extension theorems for Sobolev-type functions in metric spaces
Trace and extension theorems for Sobolev-type functions in metric spaces Open
Trace classes of Sobolev-type functions in metric spaces are subject of this paper. In particular, functions on domains whose boundary has an upper codimension-$θ$ bound are considered. Based on a Poincaré inequality, existence of a Borel …
View article: Trace and extension theorems for Sobolev-type functions in metric spaces
Trace and extension theorems for Sobolev-type functions in metric spaces Open
Trace classes of Sobolev-type functions in metric spaces are subject of this paper. In particular, functions on domains whose boundary has an upper codimension-$\theta$ bound are considered. Based on a Poincar\'e inequality, existence of a…
View article: Neumann problem for p-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity
Neumann problem for p-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity Open
We employ a variational approach to study the Neumann boundary value problem for the $p$-Laplacian on bounded smooth-enough domains in the metric setting, and show that solutions exist and are bounded. The boundary data considered are Bore…
View article: Neumann problem for p-Laplace equation in metric spaces using a\n variational approach: existence, boundedness, and boundary regularity
Neumann problem for p-Laplace equation in metric spaces using a\n variational approach: existence, boundedness, and boundary regularity Open
We employ a variational approach to study the Neumann boundary value problem\nfor the $p$-Laplacian on bounded smooth-enough domains in the metric setting,\nand show that solutions exist and are bounded. The boundary data considered are\nB…