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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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 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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An inequality for the maximum curvature through a geometric flow [PDF]
, 2015 We provide a new proof of the following inequality: the maximum curvature $k_\mathrm{max}$ and the enclosed area $A$ of a smooth Jordan curve satisfy $k_\mathrm{max}\ge \sqrt{\pi/A}$.
Pankrashkin, Konstantin
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Protection Zones in Periodic-Parabolic Problems
Advanced Nonlinear Studies, 2020 This paper characterizes whether or ...
López-Gómez Julián
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Strong Maximum Principle for Some Quasilinear Dirichlet Problems Having Natural Growth Terms
Advanced Nonlinear Studies, 2020 In this paper, dedicated to Laurent Veron, we prove that the Strong Maximum Principle holds for solutions of some quasilinear elliptic equations having lower order terms with quadratic growth with respect to the gradient of the solution.
Boccardo Lucio, Orsina Luigi
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The Moving Plane Method for Doubly Singular Elliptic Equations Involving a First-Order Term
Advanced Nonlinear Studies, 2021 In this paper we deal with positive singular solutions to semilinear elliptic problems involving a first-order term and a singular nonlinearity. Exploiting a fine adaptation of the well-known moving plane method of Alexandrov–Serrin and a careful choice ...
Esposito Francesco, Sciunzi Berardino
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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
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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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