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# đź“™ Geodetic Boundary Value Problem: the Equivalence between Molodenskyâ€™s and Helmertâ€™s Solutions by Fernando SansĂ˛, Michael G. Sideris (auth.) â€” download pdf

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This book offers a new approach to interpreting the geodetic boundary value problem, successfully obtaining the solutions of the Molodensky and Stokes boundary value problems (BVPs) with the help of downward continuation (DC) based methods. Although DC is known to be an improperly posed operation, classical methods seem to provide numerically sensible results, and therefore it can be concluded that such classical methods must in fact be manifestations of different, mathematically sound approaches.

Here, the authors first prove the equivalence of Molodenskyâ€™s and Stoke's approaches with Helmertâ€™s reduction in terms of both BVP formulation and BVP solutions by means of the DC method. They then go on to show that this is not merely a downward continuation operation, and provide more rigorous interpretations of the DC approach as a change of boundary approach and as a pseudo BVP solution approach.

- Series:
**SpringerBriefs in Earth Sciences** - Author:
**Fernando SansĂ˛, Michael G. Sideris (auth.)** - Year:
**2017** - Publisher:
**Springer International Publishing** - Language:
**English** - ISBN:
**978-3-319-46358-2,978-3-319-46357-5**

- File size:
**1 458 207** - Format:
**pdf**

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This book offers a simultaneous treatment of the theory and numerical application of boundary-value problems related to the determination of a precise geoid from gravimetric data. The following subjects are discussed: topographical effects and their compu...

Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically ri...

The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates f...

This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are...

This book covers the analysis of pseudo-differential operators on manifolds with conical points and edges. The standard singular integral operators on the half-axis as well as boundary value problems on smooth manifolds are treated as particular cone and ...

This monograph systematically treats a theory of elliptic boundary value problems in domains without singularities and in domains with conical or cuspidal points. This exposition is self-contained and a priori requires only basic knowledge of functional a...

The objective of this book is to report the results of investigations made by the authors into certain hydrodynamical models with nonlinear systems of partial differential equations.The investigations involve the results concerning Navier-Stokes equations...

This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are...

This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first ...