Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is the first volume in the field of mechanics which presents a unified method solution of contact and crack problems for a transversely isotropic elastic body. Layered media subjected to punches and cracks are also considered.Complete descriptions of the fields of stresses and strain are given, often in terms of elementary functions. Numerical methods for solving various contact and crack problems are described and accurate numerical results are presented, as necessary bench marks.The book will be of interest to graduate students in the field of mechanical and civil engineering as well as

Elasticity. --- Fracture mechanics. --- Boundary value problems. --- Contact mechanics --- Mathematical models.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on near positivity.  The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the ïrst part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenberg-type symmetry result is included. Finally, some recent progress on the Dirichlet problem for Willmore surfaces under symmetry assumptions is discussed.

Boundary value problems --- Problèmes aux limites --- Problèmes aux limites --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on “near positivity.” The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the first part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenberg-type symmetry result is included. Finally, some recent progress on the Dirichlet problem for Willmore surfaces under symmetry assumptions is discussed.

Boundary value problems --- Mathematics --- Mathematical Theory --- Calculus --- Physical Sciences & Mathematics --- Boundary value problems. --- Boundary conditions (Differential equations) --- Mathematics. --- Functional analysis. --- Differential geometry. --- Continuum mechanics. --- Mathematics, general. --- Functional Analysis. --- Differential Geometry. --- Continuum Mechanics and Mechanics of Materials. --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Differential geometry --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Global differential geometry. --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Geometry, Differential

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339-341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in three-dimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently, as surfaces of zero mean curvature. The final definition of a minimal surface is that of a nonconstant harmonic mapping X: OmegaoR^3 which is conformally parametrized on OmegasubsetR^2 and may have branch points. Thereafter the classical theory of minimal surfaces is surveyed, comprising many examples, a treatment of Björling´s initial value problem, reflection principles, a formula of the second variation of area, the theorems of Bernstein, Heinz, Osserman, and Fujimoto. The second part of this volume begins with a survey of Plateau´s problem and of some of its modifications. One of the main features is a new, completely elementary proof of the fact that area A and Dirichlet integral D have the same infimum in the class C(G) of admissible surfaces spanning a prescribed contour G. This leads to a new, simplified solution of the simultaneous problem of minimizing A and D in C(G), as well as to new proofs of the mapping theorems of Riemann and Korn-Lichtenstein, and to a new solution of the simultaneous Douglas problem for A and D where G consists of several closed components. Then basic facts of stable minimal surfaces are derived; this is done in the context of stable H-surfaces (i.e. of stable surfaces of prescribed mean curvature H), especially of cmc-surfaces (H = const), and leads to curvature estimates for stable, immersed cmc-surfaces and to Nitsche´s uniqueness theorem and Tomi´s finiteness result. In addition, a theory of unstable solutions of Plateau´s problems is developed which is based on Courant´s mountain pass lemma. Furthermore, Dirichlet´s problem for nonparametric H-surfaces is solved, using the solution of Plateau´s problem for H-surfaces and the pertinent estimates.

Boundary value problems. --- Curves, Algebraic. --- Minimal surfaces. --- Minimal surfaces --- Boundary value problems --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Calculus --- Operations Research --- Geometry --- Geometry, Differential. --- Differential geometry --- Surfaces, Minimal --- Mathematics. --- Functions of complex variables. --- Partial differential equations. --- Differential geometry. --- Calculus of variations. --- Physics. --- Calculus of Variations and Optimal Control; Optimization. --- Differential Geometry. --- Partial Differential Equations. --- Functions of a Complex Variable. --- Theoretical, Mathematical and Computational Physics. --- Maxima and minima --- Mathematical optimization. --- Global differential geometry. --- Differential equations, partial. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Complex variables --- Elliptic functions --- Functions of real variables --- Partial differential equations --- Geometry, Differential --- Mathematical physics. --- Physical mathematics --- Physics --- Isoperimetrical problems --- Variations, Calculus of

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The purpose of this book is to give a comprehensive exposition of the theory of boundary integral equations for single and double layer potentials on curves with exterior and interior cusps. The theory was developed by the authors during the last twenty years and the present volume is based on their results. The first three chapters are devoted to harmonic potentials, and in the final chapter elastic potentials are treated. Theorems on solvability in various function spaces and asymptotic representations for solutions near the cusps are obtained. Kernels and cokernels of the integral operators

Boundary element methods -- Congresses. --- Boundary element methods. --- Nonlinear theories -- Congresses. --- Nonlinear theories. --- Boundary value problems --- Boundary element methods --- Dirichlet problem --- Neumann problem --- Elasticity --- Integral equations --- Civil & Environmental Engineering --- Mathematics --- Calculus --- Operations Research --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Integral equations. --- Equations, Integral --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Mathematics. --- Integral Equations. --- Functional equations --- Functional analysis --- Numerical analysis