Generalized versus classical normal derivative [PDF]
, 2023 Given a bounded domain with Lipschitz boundary, the general Green formula permits to justify that the weak solutions of a Neumann elliptic problem satisfy the Neumann boundary condition in a weak sense.
MOTREANU, Viorica V. +3 more
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Existence and asymptotic behavior of solitary waves for a weakly coupled Schrödinger system
Advanced Nonlinear Studies, 2022 This paper deals with the following weakly coupled nonlinear Schrödinger system −Δu1+a1(x)u1=∣u1∣2p−2u1+b∣u1∣p−2∣u2∣pu1,x∈RN,−Δu2+a2(x)u2=∣u2∣2p−2u2+b∣u2∣p−2∣u1∣pu2,x∈RN,\left\{\begin{array}{ll}-\Delta {u}_{1}+{a}_{1}\left(x){u}_{1}=| {u}_{1}{| }^{2p-2 ...
An Xiaoming, Yang Jing
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Maximum Principles and ABP Estimates to Nonlocal Lane–Emden Systems and Some Consequences
Advanced Nonlinear Studies, 2021 This paper deals with maximum principles depending on the domain and ABP estimates associated to the following Lane–Emden system involving fractional Laplace operators:
Leite Edir Junior Ferreira
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Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues
Advances in Nonlinear Analysis, 2022 We consider the Dirichlet problem for partial trace operators which include the smallest and the largest eigenvalue of the Hessian matrix. It is related to two-player zero-sum differential games. No Lipschitz regularity result is known for the solutions,
Vitolo Antonio
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Maximum principle for higher order operators in general domains
Advances in Nonlinear Analysis, 2021 We first prove De Giorgi type level estimates for functions in W1,t(Ω), Ω⊂RN$ \Omega\subset{\mathbb R}^N $, with t>N≥2$ t \gt N\geq 2 $. This augmented integrability enables us to establish a new Harnack type inequality for functions which do not ...
Cassani Daniele, Tarsia Antonio
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On principal eigenvalues for periodic parabolic Steklov problems
Abstract and Applied Analysis, Volume 7, Issue 8, Page 401-421, 2002., 2002 Let Ω be a C2+γ domain in ℝN, N ≥ 2, 0 < γ < 1. Let T > 0 and let L be a uniformly parabolic operator Lu = ∂u/∂t − ∑i,j (∂/∂xi) (aij(∂u/∂xj)) + ∑jbj (∂u/∂xi) + a0u, a0 ≥ 0, whose coefficients, depending on (x, t) ∈ Ω × ℝ, are T periodic in t and satisfy some regularity assumptions.
T. Godoy, E. Lami Dozo, S. Paczka
wiley +1 more source
Nonlinear Neumann Boundary Conditions for Quasilinear Degenerate Elliptic Equations and Applications [PDF]
, 1999 We prove comparison results between viscosity sub and supersolutions of degenerate elliptic and parabolic equations associated to, possibly nonlinear, Neumann boundary conditions. These results are obtained under more general assumptions on the equation (
Barles, Guy, Guy Barles
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Uniqueness of weak solution for nonlinear elliptic equations in divergence form
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 5, Page 313-318, 2000., 2000 We study the uniqueness of weak solutions for quasilinear elliptic equations in divergence form. Some counterexamples are given to show that our uniqueness result cannot be improved in the general case.
Xu Zhang
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Some maximum principles for solutions of a class of partial differential equations in Ω ⊂ ℝn
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 11, Page 749-751, 2000., 2000 We find maximum principles for solutions of semilinear elliptic partial differential equations of the forms: (1) Δ2u + αf(u) = 0, α ∈ ℝ+ and (2) ΔΔu + α(Δu) k + gu = 0, α ≤ 0 in some region Ω ⊂ ℝn.
Mohammad Mujalli Al-Mahameed
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Maximum principles for parabolic systems coupled in both first‐order and zero‐order terms
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 813-816, 1994., 1993 Some generalized maximum principles are established for linear second‐order parabolic systems in which both first‐order and zero‐order terms are coupled.
Chiping Zhou
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