1,721,051 research outputs found
Uniqueness and representation theorems for solutions of Kolmogorov-Fokker-Planck equations
No full textWe prove the uniqueness of the solution of the Cauchy problem for a class of Kolmogorov equation
A global lower bound for the fundamental solution of Kolmogorov-Fokker-Planck equations
No full textWe prove a lower bound for the fundamental solution to a class of Kolmogorov equations. Our method relies on an invariant Harnack inequalit
On the regularity of solutions to a nonlinear ultraparabolic equation arising in mathematical finance
Full text linkWe consider the Cauchy problem relate to a nonlinear degenerate partial differential equation. We give sufficient conditions for the existence of a regular classical solutio
Bounded global solutions for a class of elliptic quasilinear equations
No full textWe prove the existence of positive solutions by non-variational method
Existence of positive solutions of quasilinear elliptic equations through nonvariational methods
No full textWe prve the existence of a positive solution by a non-varational method
Counterexample to the exponential decay for systems with memory
No full textWe prove the asymptotic devcay of the solution u to an initial andboundary value problem related to an integro-diffeerentialequation with a memory kernel. We prove that the exponential decay may occur only if the memory kernel exponentially decays
The Moser's iterative method for a class of ultraparabolic equations
No full textWe adapt the iterative scheme by Moser, to prove that the weak solutions to an ultraparabolic equation, with measurable coefficients, are locally bounded functions. Due to the strong degeneracy of the equation, our method differs from the classical one in that it is based on some ad hoc Sobolev type inequalities for solution
On a class of ultraparabolic operators of Kolmogorov-Fokker-Planck type
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A nonlinear PDE in mathematical finance
Full text linkWe study a nonlinear degenerate partial Differential Equation arising in Mathematical Finance. We prove the existence of a solution to the Cauchy problem by using the PDE's regularity theory on Lie group
A survey on the classical theory for Kolmogorov equation
Full text linkWe present a survey on the regularity theory for classic solutions to subelliptic degenerate Kolmogorov equations. In the last part of this note we present a detailed proof of a Harnack inequality and a strong maximum principle
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