6 citations · 12 across the 9 of their papers we have counts for
9 papers
Monotone methods in counterparty risk models with non-linear Black-Scholes-type equations
Bénédicte Alziary, Peter Takáč
A non-linear Black-Scholes-type equation is studied within counterparty risk models. The classical hypothesis on the uniform Lipschitz-continuity of the non-linear reaction functio…
On the Strong Comparison Principle for Degenerate Elliptic Problems with Convection
Jiří Benedikt, Petr Girg, Lukáš Kotrla +1
The weak and strong comparison principles, respectively, are investigated for quasi-linear elliptic boundary value problems with the -Laplacian in one space dimension. We treat…
The Heston stochastic volatility model has a boundary trace at zero volatility
Bénédicte Alziary, Peter Takáč
We establish boundary regularity results in Hölder spaces for the degenerate parabolic problem obtained from the Heston stochastic volatility model in Mathematical Finance set up i…
Symmetry and stability of non-negative solutions to degenerate elliptic equations in a ball
Friedemann Brock, Peter Takac
We consider non-negative distributional solutions to the equation $-\mbox{div} [g(|\nabla u|)|\nabla u|^{-1} \nabla u ] = f(|x|,u)$ in a ball , with $…
Travelling waves in the Fisher-KPP equation with nonlinear diffusion and a non-Lipschitzian reaction term
Pavel Drabek, Peter Takac
We consider a one-dimensional reaction-diffusion equation of Fisher-Kolmogoroff-Petrovsky-Piscounoff type. We investigate the effect of the interaction between the nonlinear diffus…
On maximum and comparison principles for parabolic problems with the -Laplacian
Vladimir Bobkov, Peter Takac
We investigate strong and weak versions of maximum and comparison principles for a class of quasilinear parabolic equations with the -Laplacian $$ \partial_t u - Δ_p u = λ|u|^{p…