Elliptic equation

Realistic Mathematics Education (RME) has gained popularity worldwide to teach mathematics using real-world problems. This study investigates the effectiveness of elliptic topics taught to 10th graders in a Vietnamese high school and students' attitudes toward learning.

19p viarnault 25-04-2024 2 1   Download

In this paper, we establish some gradient estimates via fractional maximal operators for a class of (p,q)-Laplace type equations in generalized Morrey spaces. The global regularity results were obtained in two steps. In the first step, we construcedt the gradient estimate in the setting of weighted Lorentz spaces.

14p vimichaelfaraday 28-12-2023 6 3   Download

In the paper "Liouville-type theorems for a quasilinear elliptic equation of the H´enon-type", We consider the H´enon-type quasilinear elliptic equation −Δmu = |x| aup where Δmu = div(|∇u| m−2∇u), m > 1, p>m − 1 and a ≥ 0. We are concerned with the Liouville property, i.e. the nonexistence of positive solutions in the whole space RN . We prove the optimal Liouville-type theorem for dimension N

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In this paper we consider spectral properties of the operator pencils generated by boundary-value problems for second order elliptic equation depending parameter in a plane angle. We receive explicit formula for the eigenvalues and the eigenvectors of the operator pencil, the multiplicity of the eigenvalues, and the differentiability of the eigenvalues and the eigenvectors with respect to the parameter.

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In this paper, we study the optimal control problems of systems governed by Klein-Gordon hemivariational inequalities. We establish the existence of solutions and the optimal control to these problems.

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In this paper, we will extend the result of Farina to the general case a0 and look for the effect of the degeneracy on the range of the exponent p on Liouville-type theorem. It seems that the presence of the weight term |x|a makes the problem more challenging. The main difficulty is that the Grushin operator is nonautonomous. This requires suitable scaled test functions in the integral estimate.

11p tamynhan9 02-12-2020 13 1   Download

oblem for a ND nonlinear elliptic equation in a bounded domain. As we know, the problem is severely ill-posed. We apply the Fourier truncation method to regularize the problem. Error estimates between the regularized solution and the exact solution are established in p H space under some priori assumptions on the exact solution.

10p gildur 30-11-2019 8 1   Download

In this paper we continue to develop the method on non-uniform grids for solving a boundary problem for elliptic equation in a semistrip.

5p vixyliton2711 12-04-2019 13 1   Download

We present the solution of a second-order nonlinear parabolic interface problem on a quasiuniform triangular finite element with a linearized four-step implicit scheme used for the time discretization. The convergence of the scheme in L2-norm is established under certain regularity assumptions using interpolation and elliptic projection operators.

16p nutifooddau 21-01-2019 23 1   Download

Part 2 Lectures In basic computational numerical analysis has contents: Numerical solution of ODEs, numerical solution of PDEs (mathematical introduction, overview of discretization methods for PDEs, elliptic equations,...).

87p bautroibinhyen20 06-03-2017 41 4   Download

(bq) part 2 book "partial differential equations in action" has contents: distributions and sobolev spaces, elements of functional analysis, variational formulation of elliptic problems, elements of functional analysis.

253p bautroibinhyen20 06-03-2017 42 5   Download

(bq) part 1 book "computational fluid dynamics for engineers" has contents: conservation equations, turbulence models, numerical methods for model parabolic and elliptic equations, numerical methods for model hyperbolic equations.

190p bautroibinhyen18 23-02-2017 31 2   Download

This book collects the lecture notes of two courses and one mini-course held in a winter school in Bologna in January 2005. The aim of this school was to popularize techniques of geometric measure theory among researchers and PhD students in hyperbolic differential equations. Though initially developed in the context of the calculus of variations, many of these techniques have proved to be quite powerful for the treatment of some hyperbolic problems.

138p coeus75 29-01-2013 48 3   Download

Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Q-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and min-max schemes, jointly with the compactness result of [35]. 1.

48p dontetvui 17-01-2013 59 7   Download

The discovery of infinite products byWallis and infinite series by Newton marked the beginning of the modern mathematical era. The use of series allowed Newton to find the area under a curve defined by any algebraic equation, an achievement completely beyond the earlier methods ofTorricelli, Fermat, and Pascal. The work of Newton and his contemporaries, including Leibniz and the Bernoullis, was concentrated in mathematical analysis and physics.

0p hotmoingay 03-01-2013 217 34   Download

What is computational physics? Here, we take it to mean techniques for simulating continuous physical systems on computers. Since mathematical physics expresses these systems as partial differential equations, an equivalent statement is that computational physics involves solving systems of partial differential equations on a computer. This book is meant to provide an introduction to computational physics to students in plasma physics and related disciplines. We present most of the basic concepts needed for numerical solution of partial differential equations.

364p thienbinh1311 13-12-2012 51 5   Download

EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR A CLASS OF DEGENERATE NONLINEAR ELLIPTIC EQUATIONS ˘ MIHAI MIHAILESCU Received 11 January 2005; Revised 4 July 2005; Accepted 17 July 2005 The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space RN . The solutions will be obtained in a subspace of the Sobolev space W 1,p (RN ). The proofs rely essentially on the Mountain Pass theorem and on Ekeland’s Variational principle. Copyright © 2006 Mihai Mih˘ ilescu.

17p sting12 10-03-2012 48 3   Download

SEMILINEAR PROBLEMS WITH BOUNDED NONLINEAR TERM MARTIN SCHECHTER Received 17 August 2004 We solve boundary value problems for elliptic semilinear equations in which no asymptotic behavior is prescribed for the nonlinear term. 1. Introduction Many authors (beginning with Landesman and Lazer [1]) have studied resonance problems for semilinear elliptic partial differential equations of the form −∆u − λ u = f (x,u) in Ω, u = 0 on ∂Ω, (1.1) where Ω is a smooth bounded domain in Rn , λ is an eigenvalue of the linear problem −∆u = λu in Ω, u = 0 on ∂Ω, (1.

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MAXIMAL REGULAR BOUNDARY VALUE PROBLEMS IN BANACH-VALUED WEIGHTED SPACE RAVI P. AGARWAL, MARTIN BOHNER, AND VELI B. SHAKHMUROV Received 10 July 2004 This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter.

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EIGENVALUE PROBLEMS FOR DEGENERATE NONLINEAR ELLIPTIC EQUATIONS IN ANISOTROPIC MEDIA ˘ DUMITRU MOTREANU AND VICENTIU RADULESCU ¸ Received 23 September 2004 and in revised form 26 November 2004 We study nonlinear eigenvalue problems of the type − div(a(x)∇u) = g(λ,x,u) in RN , where a(x) is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality.

21p sting12 10-03-2012 45 4   Download