A Schauder approach to degenerate-parabolic partial differential equations with unbounded coefficients

DOI10.1016/j.jde.2013.03.006zbMath1284.35238arXiv1112.4824OpenAlexW2054579041MaRDI QIDQ389738

Camelia A. Pop, Paul M. N. Feehan

Publication date: 21 January 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.4824

zbMATH Keywords

half-spacedegenerate diffusion processHeston stochastic volatility process

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Degenerate parabolic equations (35K65) Diffusion processes (60J60) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91)

Related Items (20)

A classical Perron method for existence of smooth solutions to boundary value and obstacle problems for degenerate-elliptic operators via holomorphic maps ⋮ Uniqueness for degenerate parabolic equations in weighted \(L^1\) spaces ⋮ On backward Kolmogorov equation related to CIR process ⋮ \(C^0\)-estimates and smoothness of solutions to the parabolic equation defined by Kimura operators ⋮ Option prices under liquidity risk as weak solutions of semilinear diffusion equations ⋮ On the martingale problem for degenerate-parabolic partial differential operators with unbounded coefficients and a mimicking theorem for Itô processes ⋮ Boundary-degenerate elliptic operators and Hölder continuity for solutions to variational equations and inequalities ⋮ Singular parabolic equations of second order on manifolds with singularities ⋮ Degenerate linear parabolic equations in divergence form on the upper half space ⋮ Boundary estimates for a degenerate parabolic equation with partial Dirichlet boundary conditions ⋮ The Heston stochastic volatility model has a boundary trace at zero volatility ⋮ Nondivergence form degenerate linear parabolic equations on the upper half space ⋮ Initial-boundary value problems for conservative Kimura-type equations: solvability, asymptotic and conservation law ⋮ \(C^{1,1}\) regularity for degenerate elliptic obstacle problems ⋮ Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations ⋮ Perturbations of local maxima and comparison principles for boundary-degenerate linear differential equations ⋮ Dirichlet boundary conditions for degenerate and singular nonlinear parabolic equations ⋮ Maximum Principles for Boundary-Degenerate Second Order Linear Elliptic Differential Operators ⋮ Integral conditions for uniqueness of solutions to degenerate parabolic equations ⋮ Stochastic representation of solutions to degenerate elliptic and parabolic boundary value and obstacle problems with Dirichlet boundary conditions

Cites Work

• Smooth zero-contact-angle solutions to a thin-film equation around the steady state
• Mimicking the one-dimensional marginal distributions of processes having an Ito differential
• Free-boundary regularity for generalized porous medium equations
• Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations
• Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations
• 2-D stability of the Néel wall
• Boundary value problems for some degenerate-elliptic operators
• Errata corrige: Boundary value problems for some degenerate-elliptic operators
• Equations with nonnegative characteristic form. I
• Equations with nonnegative characteristic form. II
• On the martingale problem for degenerate-parabolic partial differential operators with unbounded coefficients and a mimicking theorem for Itô processes
• A Free Boundary Problem of Fourth Order: Classical Solutions in Weighted Hölder Spaces
• Wright–Fisher Diffusion in One Dimension
• Elliptic and Parabolic Second-Order PDEs with Growing Coefficients
• Markovian projection onto a Heston model
• Properties of nonnegative solutions of degenerate elliptic equations
• The local regularity of solutions of degenerate elliptic equations
• Regularity of the free boundary for the porous medium equation
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• Degenerate elliptic‐parabolic equations of second order
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A Schauder approach to degenerate-parabolic partial differential equations with unbounded coefficients