Partial Regularity for Stationary Solutions to Liouville-Type Equation in Dimension 3
نویسندگان
چکیده
منابع مشابه
Partial Regularity for Stationary Solutions to Liouville - Type Equation in dimension 3 Francesca
where the function u is defined on some open subset of IR, L is a linear elliptic operator of order m and where the nonlinear operator f involves derivatives of u up to order m−1 . Once we fixe the dimension n of the underlying space and the function space V, to which the solution u is assumed to belong, equations like (1) can be classified in three categories : the sub-critical, critical and s...
متن کاملLiouville Type Results and Regularity of the Extremal Solutions of Biharmonic Equation with Negative Exponents
We first obtain Liouville type results for stable entire solutions of the biharmonic equation −∆2u = u−p in R for p > 1 and 3 ≤ N ≤ 12. Then we consider the Navier boundary value problem for the corresponding equation and improve the known results on the regularity of the extremal solution for 3 ≤ N ≤ 12. As a consequence, in the case of p = 2, we show that the extremal solution u∗ is regular w...
متن کاملPartial Regularity of Brenier Solutions of the Monge-ampère Equation
Given Ω,Λ ⊂ R two bounded open sets, and f and g two probability densities concentrated on Ω and Λ respectively, we investigate the regularity of the optimal map ∇φ (the optimality referring to the Euclidean quadratic cost) sending f onto g. We show that if f and g are both bounded away from zero and infinity, we can find two open sets Ω′ ⊂ Ω and Λ′ ⊂ Λ such that f and g are concentrated on Ω′ ...
متن کاملRegularity of the extremal solutions for the Liouville system
where λ, μ > 0 are parameters and Ω is a smoothly bounded domain of R , N ≥ 1. As shown by M. Montenegro (see [6]), there exists a limiting curve Υ in the first quadrant of the (λ, μ)-plane serving as borderline for existence of classical solutions of (1). He also proved the existence of a weak solution u∗ for every (λ∗, μ∗) on the curve Υ and left open the question of its regularity. Following...
متن کاملC regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two
We prove C regularity of c-convex weak Alexandrov solutions of a Monge-Ampère type equation in dimension two, assuming only a bound from above on the Monge-Ampère measure. The Monge-Ampère equation involved arises in the optimal transport problem. Our result holds true under a natural condition on the cost function, namely non-negative cost-sectional curvature, a condition introduced in [7], th...
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: Communications in Partial Differential Equations
سال: 2008
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605300802402625