Bounded weak solutions to nonlinear elliptic equations
نویسندگان
چکیده
منابع مشابه
Boundary Regularity of Weak Solutions to Nonlinear Elliptic Obstacle Problems
for all v∈ ={v∈W 0 (Ω), v≥ψ a.e. in Ω}. Here Ω is a bounded domain in RN (N≥2) with Lipschitz boundary, 2≤ p ≤N . A(x,ξ) :Ω×RN → RN satisfies the following conditions: (i) A is a vector valued function, the mapping x → A(x,ξ) is measurable for all ξ ∈ RN , ξ → A(x,ξ) is continuous for a.e. x ∈Ω; (ii) the homogeneity condition: A(x, tξ)= t|t|p−2A(x,ξ), t ∈ R, t = 0; (iii) the monotone inequality...
متن کاملTHE REGULARITY OF WEAK SOLUTIONS TO NONLINEAR SCALAR FIELD ELLIPTIC EQUATIONS CONTAINING p&q-LAPLACIANS
Abstract. In this paper, we consider the regularity of weak solutions u ∈ W (R ) ∩ W (R ) of the elliptic partial differential equation −∆pu−∆qu = f(x), x ∈ R , where 1 < q < p < N . We prove that these solutions are locally in C and decay exponentially at infinity. Furthermore, we prove the regularity for the solutions u ∈ W (R ) ∩W (R ) of the following equations −∆pu−∆qu = f(x, u), x ∈ R , w...
متن کاملΦ-Bounded Solutions to Nonlinear Difference Equations with Advanced Arguments
In this work we give sufficient conditions in order that the difference equation with advanced arguments x(n + 1) = A(n)x(n) + B(n)x(σ1(n)) + f(n, x(n), x(σ2(n))), σi(n) ≥ n + 1 has Φ−bounded solutions in the space `Φ of Φ−bounded sequences, are given.
متن کاملEntire Solutions to a Class of Fully Nonlinear Elliptic Equations
We study nonlinear elliptic equations of the form F (Du) = f(u) where the main assumption on F and f is that there exists a one dimensional solution which solves the equation in all the directions ξ ∈ Rn. We show that entire monotone solutions u are one dimensional if their 0 level set is assumed to be Lipschitz, flat or bounded from one side by a hyperplane.
متن کاملSmooth approximations to solutions of nonconvex fully nonlinear elliptic equations
We show that fully nonlinear elliptic PDEs (which may not have classical solutions) can be approximated with integro-differential equations which have C solutions. For these approximated equation we prove a uniform C estimate. We also study the rate of convergence.
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: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2009
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2009.1.10