On angularly perturbed Laplace equations in the unit ball and their distributional boundary values

1999 ◽  
pp. 359-377
Author(s):  
Peter R. Massopust
Keyword(s):  
Unit Ball ◽  
Boundary Values ◽  
Laplace Equations

scholarly journals Existence and Uniqueness of Solutions for a Class of p-Laplace Equations on a Ball

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Philip Korman
Keyword(s):  
Unit Ball ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Model Case ◽  
Laplace Equations

AbstractFor a class of equations generalizing the model caseΔwhere B is the unit ball in R

scholarly journals Simply Supported Biharmonic Equations with Polynomial Data in The Unit Ball of $ R^n$

2018 ◽  
Author(s):  
Agah D. Garnadi
Keyword(s):  
Unit Ball ◽  
Dirichlet Boundary ◽  
Exact Algorithms ◽  
Dirichlet Boundary Conditions ◽  
Polynomial Functions ◽  
Dirichlet Problems ◽  
Biharmonic Equations ◽  
Simply Supported ◽  
Poisson Equations ◽  
Laplace Equations

We studied simply supported boundary value problem of Biharmonic equation in the unit ball of $R^n, n \geq 3,$ with polynomial data. The problem is restated as a pair of Laplace and Poisson equations with polynomial Dirichlet problems. We utilize an exact algorithms for solving Laplace equations with Dirichlet boundary conditions with polynomial functions data. The algorithm requires only differentiation of the boundary data, but no integration

scholarly journals Polyharmonic Problems with Simply Supported Polynomial Data in the Unit Ball in $ R^n$

2018 ◽  
Author(s):  
Agah D. Garnadi
Keyword(s):  
Boundary Value Problem ◽  
Unit Ball ◽  
Poisson Equation ◽  
Boundary Function ◽  
Exact Algorithms ◽  
Dirichlet Problems ◽  
Polyharmonic Equation ◽  
Dirichlet Conditions ◽  
Simply Supported ◽  
Laplace Equations

We studied simply supported polynomial data of boundary value problem of Polyharmonic equation. The problem is reformulated as a systems of Laplace-Poisson equation with Polynomial Dirichlet problems. We utilize an exact algorithms for solving Laplace equations with Dirichlet conditions with polynomial data. The algorithm requires differentiation of the boundary function, but no integration.

Estimates for Convex Integral Means of Harmonic Functions

2013 ◽  
Vol 57 (3) ◽  
pp. 619-630
Author(s):  
Dimitrios Betsakos
Keyword(s):  
Harmonic Function ◽  
Unit Ball ◽  
Unit Sphere ◽  
Harmonic Functions ◽  
Integrable Function ◽  
Right Hemisphere ◽  
Boundary Values ◽  
Integral Means ◽  
Decreasing Rearrangement ◽  
The Right

AbstractWe prove that if f is an integrable function on the unit sphere S in ℝn, g is its symmetric decreasing rearrangement and u, v are the harmonic extensions of f, g in the unit ball , then v has larger convex integral means over each sphere rS, 0 < r < 1, than u has. We also prove that if u is harmonic in with |u| < 1 and u(0) = 0, then the convex integral mean of u on each sphere rS is dominated by that of U, which is the harmonic function with boundary values 1 on the right hemisphere and −1 on the left one.

Solutions of p-Laplace Equations with Infinite Boundary Values: The case of Non-Autonomous and Non-Monotone Nonlinearities

2015 ◽  
Vol 59 (4) ◽  
pp. 959-987 ◽  
Author(s):  
Michael A. Karls ◽  
Ahmed Mohammed
Keyword(s):  
Continuous Function ◽  
Boundary Value Problem ◽  
Growth Conditions ◽  
Monotonicity Condition ◽  
Inhomogeneous Term ◽  
Boundary Values ◽  
Bounded Smooth Domain ◽  
Laplace Equations ◽  
Bounded Smooth ◽  
Image Position

AbstractFor a non-negative and non-trivial real-valued continuous function hΩ × [0, ∞) such that h(x, 0) = 0 for all x ∈ Ω, we study the boundary-value problemwhere Ω ⊆ ℝN, N ⩾ 2, is a bounded smooth domain and Δp:= div(|Du|p–2DDu) is the p-Laplacian. This work investigates growth conditions on h(x, t) that would lead to the existence or non-existence of distributional solutions to (BVP). In a major departure from past works on similar problems, in this paper we do not impose any special structure on the inhomogeneous term h(x, t), nor do we require any monotonicity condition on h in the second variable. Furthermore, h(x, t) is allowed to vanish in either of the variables.

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