Gradient estimates for Neumann boundary value problem of Monge-Ampère type equations on Riemannian manifolds

2017 ◽  
Vol 150 ◽  
pp. 151-158 ◽  
Author(s):  
Xi Guo ◽  
Ni Xiang
Keyword(s):  
Boundary Value Problem ◽  
Riemannian Manifolds ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Gradient Estimates ◽  
Neumann Boundary Value Problem ◽  
Monge Ampere

scholarly journals The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge-Ampère Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Juan Wang ◽  
Jinlin Yang ◽  
Xinzhi Liu
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Elliptic Equation ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Type Problem ◽  
Neumann Boundary Value Problem ◽  
Nonlinear Elliptic ◽  
Nonlinear Parabolic ◽  
Neumann Type ◽  
Monge Ampere

We consider the existence, uniqueness, and asymptotic behavior of a classical solution to the initial and Neumann boundary value problem for a class nonlinear parabolic equation of Monge-Ampère type. We show that such solution exists for all times and is unique. It converges eventually to a solution that satisfies a Neumann type problem for nonlinear elliptic equation of Monge-Ampère type.

scholarly journals POSITIVE SOLUTIONS OF A SECOND-ORDER NEUMANN BOUNDARY VALUE PROBLEM WITH A PARAMETER

2012 ◽  
Vol 86 (2) ◽  
pp. 244-253 ◽  
Author(s):  
YANG-WEN ZHANG ◽  
HONG-XU LI
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Existence And Uniqueness Theorem ◽  
Neumann Boundary Value Problem ◽  
Image Position ◽  
Continuous Dependence Of Solutions

AbstractIn this paper, we consider the Neumann boundary value problem with a parameter λ∈(0,∞): By using fixed point theorems in a cone, we obtain some existence, multiplicity and nonexistence results for positive solutions in terms of different values of λ. We also prove an existence and uniqueness theorem and show the continuous dependence of solutions on the parameter λ.

Nonlinear Neumann boundary value problem for semilinear heat equations with critical power nonlinearities

2021 ◽  
pp. 1-35
Author(s):  
Nakao Hayashi ◽  
Elena I. Kaikina ◽  
Pavel I. Naumkin ◽  
Takayoshi Ogawa
Keyword(s):  
Boundary Value Problem ◽  
Large Time ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Asymptotic Behavior Of Solutions ◽  
Heat Equations ◽  
Semilinear Heat Equation ◽  
Neumann Boundary Value Problem ◽  
Time Existence ◽  
Time Asymptotic Behavior

We study the nonlinear Neumann boundary value problem for semilinear heat equation ∂ t u − Δ u = λ | u | p , t > 0 , x ∈ R + n , u ( 0 , x ) = ε u 0 ( x ) , x ∈ R + n , − ∂ x u ( t , x ′ , 0 ) = γ | u | q ( t , x ′ , 0 ) , t > 0 , x ′ ∈ R n − 1 where p = 1 + 2 n , q = 1 + 1 n and ε > 0 is small enough. We investigate the life span of solutions for λ , γ > 0. Also we study the global in time existence and large time asymptotic behavior of solutions in the case of λ , γ < 0 and ∫ R + n u 0 ( x ) d x > 0.

The treatment of a Neumann boundary value problem for force-free fields by an integral equation method

1978 ◽  
Vol 82 (1-2) ◽  
pp. 71-86 ◽  
Author(s):  
Rainer Kress
Keyword(s):  
Integral Equation ◽  
Boundary Value Problem ◽  
Vector Fields ◽  
Integral Formula ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Integral Equation Method ◽  
Equation Method ◽  
Fredholm Alternative ◽  
Neumann Boundary Value Problem

SynopsisA Neumann boundary value problem for the equation rot μ − λμ = u is considered. The approach is by an integral equation method based on Cauchy's integral formula for generalized harmonic vector fields. Results on existence and uniqueness are obtained in terms of the familiar Fredholm alternative.

scholarly journals The Laplace equation in the exterior of the Hankel contour and novel identities for hypergeometric functions

2013 ◽  
Vol 469 (2157) ◽  
pp. 20130081 ◽  
Author(s):  
A. S. Fokas ◽  
M. L. Glasser
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Laplace Equation ◽  
Special Functions ◽  
Boundary Value ◽  
Zeta Functions ◽  
Neumann Boundary ◽  
Neumann Boundary Value Problem ◽  
Wide Range ◽  
Definition Of

By using conformal mappings, it is possible to express the solution of certain boundary-value problems for the Laplace equation in terms of a single integral involving the given boundary data. We show that such explicit formulae can be used to obtain novel identity for special functions. A convenient tool for deriving this type of identity is the so-called global relation , which has appeared recently in a wide range of boundary-value problems. As a concrete application, we analyse the Neumann boundary-value problem for the Laplace equation in the exterior of the Hankel contour, which appears in the definition of both the gamma and the Riemann zeta functions. By using the explicit solution of this problem, we derive a number of novel identities involving the hypergeometric function. Also, we point out an interesting connection between the solution of the above Neumann boundary-value problem for a particular set of Neumann data and the Riemann hypothesis.

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