Small Perturbation Solutions for Parabolic Equations

2011/11/25 by Wang, Yu · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1111.5888

Abstract

Let ϕ be a smooth solution of the parabolic equation F(D²u, Du, u, x, t)- u_t = 0: Assume F is uniform elliptic only in a neighborhood of (D²ϕ, Dϕ, ϕ, x, t), we prove that any solution obtained from small L1-perturbation of ϕ remains smooth.

Cited by

• Note on Regularity theory for Nonlinear elliptic equations
• ABP estimate and Harnack inequality for a class of degenerate fully nonlinear pseudo-p-Laplacian equations
• A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications

Related

• On the smallness of mean oscillations and regularity of weak solutions to regular/degenerate strongly coupled parabolic systems
• Interior Calderón-Zygmund estimates for solutions to general parabolic equations of p-Laplacian type
• On a Small Elliptic Perturbation of a Backward-Forward Parabolic Problem, with Applications to Stochastic Models
• A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications
• Perturbation theory for the parabolic Regularity and Neumann problem