1 citations · 2 across the 5 of their papers we have counts for
6 papers
Non-quasicontinuous Newtonian functions and outer capacities based on Banach function spaces
Anders Björn, Jana Björn, Lukáš Malý
We construct various examples of Sobolev-type functions, defined via upper gradients in metric spaces, that fail to be quasicontinuous or weakly quasicontinuous. This is done with…
Standalone Neural ODEs with Sensitivity Analysis
Rym Jaroudi, Lukáš Malý, Gabriel Eilertsen +3
This paper presents the Standalone Neural ODE (sNODE), a continuous-depth neural ODE model capable of describing a full deep neural network. This uses a novel nonlinear conjugate g…
An Analog of the Neumann Problem for the -Laplace Equation in the Metric Setting: Existence, Boundary Regularity, and Stability
Panu Lahti, Lukas Maly, Nageswari Shanmugalingam
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…
Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient
Panu Lahti, Lukas Maly, Nageswari Shanmugalingam +1
We study the geometry of domains in complete metric measure spaces equipped with a doubling measure supporting a -Poincaré inequality. We propose a notion of \emph{domain with b…
Neumann problem for p-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity
Lukáš Malý, Nageswari Shanmugalingam
We employ a variational approach to study the Neumann boundary value problem for the -Laplacian on bounded smooth-enough domains in the metric setting, and show that solutions e…
Regularization of Newtonian functions via weak boundedness of maximal operators
Lukáš Malý
Density of Lipschitz functions in Newtonian spaces based on quasi-Banach function lattices is discussed. Newtonian spaces are first-order Sobolev-type spaces on abstract metric mea…