Regularity of the solutions to a nonlinear boundary problem with indefinite weight

Existence of Solutions for Quasilinear Elliptic Equations with Nonlinear Boundary Conditions and Indefinite Weight

In this article, we establish the existence and non-existence of solutions for quasilinear equations with nonlinear boundary conditions and indefinite weight. Our proofs are based on variational methods and their geometrical features. In addition, we prove that all the weak solutions are in C1,β(Ω) for some β ∈ (0, 1).

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

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...

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Boundary Regularity for Viscosity Solutions of Fully Nonlinear Elliptic Equations

We provide regularity results at the boundary for continuous viscosity solutions to nonconvex fully nonlinear uniformly elliptic equations and inequalities in Euclidian domains. We show that (i) any solution of two sided inequalities with Pucci extremal operators is C1,α on the boundary; (ii) the solution of the Dirichlet problem for fully nonlinear uniformly elliptic equations is C2,α on the b...