30 citations · 87 across the 11 of their papers we have counts for
14 papers
A Boundary Estimate for Singular Parabolic Diffusion Equations
Ugo Gianazza, Naian Liao, Teemu Lukkari
We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of p-laplacian type. The esti…
The equivalence of weak and very weak supersolutions to the porous medium equation
Pekka Lehtelä, Teemu Lukkari
We prove that various notions of supersolutions to the porous medium equation are equivalent under suitable conditions. More spesifically, we consider weak supersolutions, very wea…
A comparison principle for the porous medium equation and its consequences
Benny Avelin, Teemu Lukkari
We prove a comparison principle for the porous medium equation in more general open sets in than space-time cylinders. We apply this result in two related contex…
A posteriori error estimates for Webster's equation in wave propagation
Teemu Lukkari, Jarmo Malinen
We consider a generalised Webster's equation for describing wave propagation in curved tubular structures such as variable diameter acoustic wave guides. Webster's equation in gene…
Stability of degenerate parabolic Cauchy problems
Teemu Lukkari, Mikko Parviainen
We prove that solutions to Cauchy problems related to the -parabolic equations are stable with respect to the nonlinearity exponent . More specifically, solutions with a fixe…
Perron's method for the porous medium equation
Juha Kinnunen, Peter Lindqvist, Teemu Lukkari
This work extends Perron's method for the porous medium equation in the slow diffusion case. The main result shows that nonnegative continuous boundary functions are resolutive in…
Lower semicontinuity of weak supersolutions to the porous medium equation
Benny Avelin, Teemu Lukkari
Weak supersolutions to the porous medium equation are defined by means of smooth test functions under an integral sign. We show that nonnegative weak supersolutions become lower se…
Acoustic wave guides as infinite-dimensional dynamical systems
Atte Aalto, Teemu Lukkari, Jarmo Malinen
We prove the unique solvability, passivity/conservativity and some regularity results of two mathematical models for acoustic wave propagation in curved, variable diameter tubular…
Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces
Alexandre Almeida, Petteri Harjulehto, Peter Hästö +1
We prove optimal integrability results for solutions of the -Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz…
Local approximation of superharmonic and superparabolic functions in nonlinear potential theory
Juha Kinnunen, Teemu Lukkari, Mikko Parviainen
We prove that arbitrary superharmonic functions and superparabolic functions related to the -Laplace and the -parabolic equations are locally obtained as limits of supersolut…
Stability of solutions to nonlinear diffusion equations
Teemu Lukkari
We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power : solutions with fixed data con…
Webster's equation with curvature and dissipation
Teemu Lukkari, Jarmo Malinen
Wave propagation in curved tubular domains is considered. A general version of Webster's equation is derived from the scattering passive wave equation. More precisely, it is shown…
Equivalence of Viscosity and Weak Solutions for the -Laplacian
Petri Juutinen, Teemu Lukkari, Mikko Parviainen
We consider different notions of solutions to the -Laplace equation $-÷(\abs{Du(x)}^{p(x)-2}Du(x))=0$ with . We show by proving a comparison principle that vi…
A Curious Equation Involving the Infinity-Laplacian
Peter Lindqvist, Teemu Lukkari
We prove the uniqueness for viscosity solutions of a differential equation involving the infinity-Laplacian with a variable exponent. A version of the Harnack's inequality is deriv…