6 edition of The oblique derivative problem of potential theory found in the catalog.
Published
1989
by Consultants Bureau in New York
.
Written in English
Edition Notes
| Statement | A.I. Yanushauskas ; translated from Russian by Norman Stein. |
| Series | Contemporary Soviet mathematics |
| Classifications | |
|---|---|
| LC Classifications | QA374 .I2613 1989 |
| The Physical Object | |
| Pagination | viii, 251 p. ; |
| Number of Pages | 251 |
| ID Numbers | |
| Open Library | OL2182863M |
| ISBN 10 | 0306110237 |
| LC Control Number | 89000595 |
Georges Julien Giraud (22 July – 16 March ) was a French mathematician, working in potential theory, partial differential equations, singular integrals and singular integral equations: he is mainly known for his solution of the regular oblique derivative problem and also for his extension to n –dimensional (n ≥ 2) singular integral equations of the concept of symbol of a singular integral, Doctoral advisor: Charles Émile Picard. The oblique derivative problem II Bengt Winzell* O. Introduction Let f2 be a bounded domain in R n, n=>3, of class C ~+~ and consider a unit vector field 1 on the boundary 0f2. We will consider the following boundary value problem for the second order elliptic operator 5e in f2: Find a solution of 5fu=g.
Other problems for elliptic semi-linear equations were considered by Veron et al., see e.g. [2, 12, 28]. The oblique derivative problem plays a major role in the study of re ected shocks in transonic ow [9]. Another important application of this theory is the capillary problem (see e.g. [14]). In geodesy, the most fundamental problems of the File Size: KB. Summary This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author.
Preliminaries --Laplace's Equation --The Dirichlet Problem --Green Functions --Negligible Sets --Dirichlet Problem for Unbounded Regions --Energy --Interpolation and Monotonicity --Newtonian Potential --Elliptic Operators --Apriori Bounds --Oblique Derivative Problem --Application to Diffusion Processes. the derivative in the equation. Solving an equation like this on an interval t2[0;T] would mean nding a functoin t7!u(t) 2R with the property that uand its derivatives intertwine in such a way that this equation is true for all values of t2[0;T]. The problem can be enlarged by replacing the real-valued uby a vector-valued one u(t) = (u 1(t);u 2.
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The Oblique Derivative Problem of Potential Theory (Monographs The oblique derivative problem of potential theory book Contemporary Mathematics) Softcover reprint of the original 1st ed. Edition by A.T. Yanushauakas (Author)Format: Paperback.
Overview. An important part of the theory of partial differential equations is the theory of boundary problems for elliptic equations and systems of equations. Among such problems those of greatest interest are the so-called non-Fredholm boundary prob lems, whose investigation reduces, as a rule, to the study of singular integral equa tions, where the Fredholm alternative is violated for these problems.
An important part of the theory of partial differential equations is the theory of boundary problems for elliptic equations and systems of equations. Among such problems those of greatest interest are the so-called non-Fredholm boundary prob lems, whose investigation reduces, as a rule, to theBrand: Springer US.
Buy An Alternative Approach to the Oblique Derivative Problem in Potential Theory (Berichte aus der Mathematik) on FREE SHIPPING on qualified orders An Alternative Approach to the Oblique Derivative Problem in Potential Theory (Berichte aus der Mathematik): Bauer, Frank: : BooksCited by: Oblique derivative problem of potential theory.
New York: Consultants Bureau, © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Alʹgimantas Ionosovich I︠A︡nushauskas.
oblique derivative problem when the vector field of the problem is tangent to the boundary of a domain on some subset. This is a typical degenerate elliptic boundary problem. The Dirichlet problem for an elliptic operator was solved in Chapter 9 by morphing a solution of the Dirichlet problem for the Laplacian on a ball into a solution of the Dirichlet problem for an elliptic operator on a ball.
In applying the method of continuity, it was necessary to show that an elliptic operator with a suitably restricted domain and range is a bounded : Lester L. Helms. facing. This is a physically motivated description of the oblique derivative problem, now we will give a mathematical one.
Definitions Let V be in an appropriate function space S defined on Σext ⊂ RN. This V will be the function we are seeking for. A mth order differential operator ∆ in Σ ext is defined as ∆ = X |µ|≤m Aµ∂µCited by: Having proved in Chapter 9 that the Dirichlet problem on a spherical chip subject to a normal derivative condition on the flat portion of the boundary and a Dirichlet type condition on the remaining portion has a solution, it is shown that such a solution can be morphed onto a local solution of an elliptic equation on a neighborhood of a boundary point satisfying mixed boundary : Lester L.
Helms. Anal. ; –62 and Bauer, An Alternative Approach to the Oblique Derivative Problem in Potential Theory, Shaker Verlag, Aachen, )). Do you want to read the rest of this article. The paper presents a novel original upwindbased approach for solving the oblique derivative boundary value problem by the finite volume method.
In this approach, the oblique derivative boundary. New & Forthcoming Titles | Monographs in Contemporary Mathematics - Formerly Contemporary Soviet Mathematics. Books & CD ROMs Show all 10 results.
The Oblique Derivative Problem of Potential Theory. We establish optimal uniform estimates in the maximum norm, for solutions of Poisson's equation, with right hand side in Lebesgue spaces, under mixed Dirichlet-oblique derivative boundary conditions, where the oblique vector is required to remain uniformly transverse, and the estimates depend only on the transversality constant, but not on the regularity of the oblique by: 6.
Normal derivative of a harmonic function at a boundary point 20 Essential spectrum of a perturbed polyharmonic operator 20 Singularity of Green’s function for second order elliptic equations with lower order terms 21 Generic degenerating oblique derivative problem 21 Matrix generalization of the oblique.
System Upgrade on Tue, May 19th, at 2am (ET) During this period, E-commerce and registration of new users may not be available for up to 12 hours. alternate approach oblique derivative problem potential theory satellite mission many people important literature interesting lecture course valuable idea symbolical solution partial differential equation fertile discussion inverse problem valuable discus-sions cooperation partner dr detailed question ill-posed problem.
The author wrote an excellent book on potential theory [1], which concentrated on harmonic oblique derivative problems. After giving the fundamental Hopf maximum principle, the Book review / Journal of Approximation Theory () – 4) The problem with oblique derivative arises when the normal derivative in condition (*) is replaced by the derivative with respect to an arbitrary direction.
In addition to these general problems, the following specific problems have also arisen in potential theory. 5) The Robin it is required to find a mass distribution on with a constant potential in the interior of.
An Alternate Approach to the Oblique Derivative Problem in Potential Theory. By Frank Bauer, Vom Fachbereich Mathematik, Der Universität Kaiserslautern and Doktor Der Naturwissenschaften. Abstract. This thesis has evolved with the advice, feedback and help of many people.
In particular I would like to express my gratitude to Prof. ADVANCES IN MATHEMAT () The Perron Process Applied to Oblique Derivative Problems GARY M. LIEBERMAN Department of Mathematics, Iowa State University, Ames, Iowa The Perron process has been used with great success to prove the solvability of the Dirichlet problem for linear elliptic equations by elementary by:.
Potential theory concerns itself primarily with the study of harmonic functions — their existence, uniqueness, and structure under various conditions. The book concludes with constructing solutions of more general elliptic equations beyond the Laplacian and discusses the oblique derivative problem, a generalization of the Neumann problem.Oblique derivative problems Gary M.
Lieberman Outline Introduction Basic Ideas Outline of future lectures Pointwise estimates We’ll start with the theory for linear problems. As for the Dirichlet problem, we want to prove, eventually, that solutions are in H 2+ () under suitable hypotheses.
But, in order toFile Size: KB.The possibility of eliminating from this representation either the scalar potential or a rectangular component of the vector potential is examined. Earlier work is discussed and the connection is made with the oblique derivative problem of potential by: 9.
