Singular Solutions to Monge-Ampère Equation
نویسندگان
چکیده
منابع مشابه
Continuity Estimates for the Monge-Ampère Equation
In this paper, we study the regularity of solutions to the Monge-Ampère equation. We prove the log-Lipschitz continuity for the gradient under certain assumptions. We also give a unified treatment for the continuity estimates of the second derivatives. As an application we show the local existence of continuous solutions to the semi-geostrophic equation arising in meteorology.
متن کاملQuaternionic Monge-ampère Equations
The main result of this paper is the existence and uniqueness of solution of the Dirichlet problem for quaternionic Monge-Ampère equations in quaternionic strictly pseudoconvex bounded domains in H. We continue the study of the theory of plurisubharmonic functions of quaternionic variables started by the author at [2].
متن کاملExplicit multiple singular periodic solutions and singular soliton solutions to KdV equation
Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...
متن کاملA note on Monge-Ampère Keller-Segel equation
This note studies the Monge–Ampère Keller–Segel equation in a periodic domain Td(d ≥ 2), a fully nonlinear modification of the Keller–Segel equation where the Monge–Ampère equation det(I + ∇2v) = u + 1 substitutes for the usual Poisson equation ∆v = u. The existence of global weak solutions is obtained for this modified equation. Moreover, we prove the regularity in L∞ 0, T ;L∞ ∩W 1,1+γ(Td) ...
متن کاملC0 penalty methods for the fully nonlinear Monge-Ampère equation
In this paper, we develop and analyze C0 penalty methods for the fully nonlinear Monge-Ampère equation det(D2u) = f in two dimensions. The key idea in designing our methods is to build discretizations such that the resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then able to show the well-posedness of the penalty method as well a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Analysis in Theory and Applications
سال: 2022
ISSN: ['1672-4070', '1573-8175']
DOI: https://doi.org/10.4208/ata.oa-0023