61 citations · 217 across the 16 of their papers we have counts for
10 papers · 1 filter
Characterizations of sets of finite perimeter using heat kernels in metric spaces
Niko Marola, Michele Miranda, Nageswari Shanmugalingam
The overarching goal of this paper is to link the notion of sets of finite perimeter (a concept associated with -spaces) and the theory of heat semigroups (a concept relat…
Phragmén-Lindelöf theorem for infinity harmonic functions
Seppo Granlund, Niko Marola
We investigate a version of the Phragmén-Lindelöf theorem for solutions of the equation in unbounded convex domains. The method of proof is to consider this infinity…
Arithmetic three-spheres theorems for quasilinear Riccati type inequalities
Seppo Granlund, Niko Marola
We consider arithmetic three-spheres inequalities to solutions of certain second order quasilinear elliptic differential equations and inequalities with a Riccati-type drift term.
Boundary measures, generalized Gauss-Green formulas, and mean value property in metric measure spaces
Niko Marola, Michele Miranda, Nageswari Shanmugalingam
We study mean value properties of harmonic functions in metric measure spaces. The metric measure spaces we consider have a doubling measure and support a (1,1)- Poincaré inequalit…
On the Harnack inequality for parabolic minimizers in metric measure spaces
Niko Marola, Mathias Masson
In this note we consider problems related to parabolic partial differential equations in geodesic metric measure spaces, that are equipped with a doubling measure and a Poincaré in…
Some remarks on sign changing solutions of a quasilinear elliptic equation in two variables
Seppo Granlund, Niko Marola
We consider planar solutions to certain quasilinear elliptic equations subject to the Dirichlet boundary conditions; the boundary data is assumed to have finite number of relative…
Vanishing properties of sign changing solutions to p-Laplace type equations in the plane
Seppo Granlund, Niko Marola
We study the nonlinear eigenvalue problem for the p-Laplacian, and more general problem constituting the Fucik spectrum. We are interested in some vanishing properties of sign chan…
On a frequency function approach to the unique continuation principle
Seppo Granlund, Niko Marola
In this survey we discuss the frequency function method so as to study the problem of unique continuation for elliptic partial differential equations. The methods used in the note…
On the problem of unique continuation for the p-Laplace equation
Seppo Granlund, Niko Marola
We study if two different solutions of the -Laplace equation where , can coincide in an open subset of their common doma…
Local behavior of p-harmonic Green's functions in metric spaces
Donatella Danielli, Nicola Garofalo, Niko Marola
We describe the behavior of p-harmonic Green's functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincaré inequality.