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Author: Enrico Valdinoci Publisher: American Mathematical Soc. ISBN: 0821858521 Category : Differential equations, Elliptic Languages : en Pages : 152
Book Description
This volume contains contributions from the INdAM School on Symmetry for Elliptic PDEs, which was held May 25-29, 2009, in Rome, Italy. The school marked ``30 years after a conjecture of De Giorgi, and related problems'' and provided an opportunity for experts to discuss the state of the art and open questions on the subject. Motivated by the classical rigidity properties of the minimal surfaces, De Giorgi proposed the study of the one-dimensional symmetry of the monotone solutions of a semilinear, elliptic partial differential equation. Impressive advances have recently been made in this field, though many problems still remain open. Several generalizations to more complicated operators have attracted the attention of pure and applied mathematicians, both for their important theoretical problems and for their relation, among others, with the gradient theory of phase transitions and the dynamical systems.
Author: Enrico Valdinoci Publisher: American Mathematical Soc. ISBN: 0821858521 Category : Differential equations, Elliptic Languages : en Pages : 152
Book Description
This volume contains contributions from the INdAM School on Symmetry for Elliptic PDEs, which was held May 25-29, 2009, in Rome, Italy. The school marked ``30 years after a conjecture of De Giorgi, and related problems'' and provided an opportunity for experts to discuss the state of the art and open questions on the subject. Motivated by the classical rigidity properties of the minimal surfaces, De Giorgi proposed the study of the one-dimensional symmetry of the monotone solutions of a semilinear, elliptic partial differential equation. Impressive advances have recently been made in this field, though many problems still remain open. Several generalizations to more complicated operators have attracted the attention of pure and applied mathematicians, both for their important theoretical problems and for their relation, among others, with the gradient theory of phase transitions and the dynamical systems.
Author: Alberto Farina Publisher: American Mathematical Soc. ISBN: 0821848046 Category : Mathematics Languages : en Pages : 152
Book Description
Contains contributions from the INdAM School on Symmetry for Elliptic PDEs, which marked ""30 years after a conjecture of De Giorgi, and related problems"" and provided an opportunity for experts to discuss the state of the art and open questions on the subject.
Author: Messoud Efendiev Publisher: Springer ISBN: 3319984071 Category : Mathematics Languages : en Pages : 258
Book Description
This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.
Author: James Eells Publisher: Princeton University Press ISBN: 9780691102498 Category : Mathematics Languages : en Pages : 238
Book Description
The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.
Author: Michel Chipot Publisher: Elsevier ISBN: 0080560598 Category : Mathematics Languages : en Pages : 618
Book Description
This handbook is the sixth and last volume in the series devoted to stationary partial differential equations. The topics covered by this volume include in particular domain perturbations for boundary value problems, singular solutions of semilinear elliptic problems, positive solutions to elliptic equations on unbounded domains, symmetry of solutions, stationary compressible Navier-Stokes equation, Lotka-Volterra systems with cross-diffusion, and fixed point theory for elliptic boundary value problems. * Collection of self-contained, state-of-the-art surveys * Written by well-known experts in the field * Informs and updates on all the latest developments
Author: Vladimir Maz'ya Publisher: Birkhäuser ISBN: 3319470795 Category : Mathematics Languages : en Pages : 313
Book Description
This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.
Author: Kari Astala Publisher: Princeton University Press ISBN: 9780691137773 Category : Mathematics Languages : en Pages : 708
Book Description
This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.
Author: George W. Bluman Publisher: Springer Science & Business Media ISBN: 0387680284 Category : Mathematics Languages : en Pages : 415
Book Description
This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.
Author: Garrett Birkhoff Publisher: SIAM ISBN: 0898710014 Category : Mathematics Languages : en Pages : 93
Book Description
A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing?the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering.
Author: Enrico Valdinoci
Author: Enrico Valdinoci
Author: Alberto Farina
Author: L. E. Fraenkel
Author: Messoud Efendiev
Author: James Eells
Author: Michel Chipot
Author: Vladimir Maz'ya
Author: Kari Astala
Author: George W. Bluman
Author: Garrett Birkhoff