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Function Spaces and Potential Theory

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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 821/5 ( reviews)

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Book Synopsis Function Spaces and Potential Theory by : David R. Adams

Download or read book Function Spaces and Potential Theory written by David R. Adams. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: "..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society

Nonlinear Potential Theory and Weighted Sobolev Spaces

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Release : 2007-05-06
Genre : Mathematics
Kind : eBook
Book Rating : 684/5 ( reviews)

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Book Synopsis Nonlinear Potential Theory and Weighted Sobolev Spaces by : Bengt O. Turesson

Download or read book Nonlinear Potential Theory and Weighted Sobolev Spaces written by Bengt O. Turesson. This book was released on 2007-05-06. Available in PDF, EPUB and Kindle. Book excerpt: The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.

Transitional Objects and Potential Spaces

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Release : 1993
Genre : Literary Criticism
Kind : eBook
Book Rating : 732/5 ( reviews)

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Book Synopsis Transitional Objects and Potential Spaces by : Peter L. Rudnytsky

Download or read book Transitional Objects and Potential Spaces written by Peter L. Rudnytsky. This book was released on 1993. Available in PDF, EPUB and Kindle. Book excerpt: D. W. Winnicott is increasingly recognized as one of the most important psychoanalysts since Freud, but the relevance of his Independent version of object relations theory to psychoanalytic literary criticism has not been sufficiently appreciated. As Peter L. Rudnytsky notes, "There must be ten literary critics conversant with Lacan's ecrits for every one who has read Winnicott's Playing and Reality." Transitional Objects and Potential Spaces begins to redress this imbalance. The title and subtitle of this collection highlight three of Winnicott's key concepts: transitional objects, potential space, and the use of an object. Because Winnicott is unique in respecting the integrity of art as an autonomous human activity while continuing to insist on its infantile origins, he may be said to offer the first adequate psychoanalytic account of aesthetics. This volume is organized into three sections: The Analytic Frame, Literary Objects, and Cultural Fields. Beginning with Winnicott's "The Location of Cultural Experience," it features essays by a distinguished group of contributors, including Marion Milner and two current leading members of the British Psycho-Analytical Society, Christopher Bollas and Patrick J. Casement, as well as such eminent critics as Richard Poirier, Murray M. Schwartz, Ellen Handler Spitz, and Madelon Sprengnether. Transitional Objects and Potential Spaces makes a timely and persuasive case for the power of Winnicott's ideas. In defining for the first time an independent tradition of psychoanalytic criticism, it will reorient future work in literary and cultural studies.

Potential Theory on Harmonic Spaces

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Release : 2012-01-16
Genre : Mathematics
Kind : eBook
Book Rating : 343/5 ( reviews)

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Book Synopsis Potential Theory on Harmonic Spaces by : Corneliu Constantinescu

Download or read book Potential Theory on Harmonic Spaces written by Corneliu Constantinescu. This book was released on 2012-01-16. Available in PDF, EPUB and Kindle. Book excerpt: There has been a considerable revival of interest in potential theory during the last 20 years. This is made evident by the appearance of new mathematical disciplines in that period which now-a-days are considered as parts of potential theory. Examples of such disciplines are: the theory of Choquet capacities, of Dirichlet spaces, of martingales and Markov processes, of integral representation in convex compact sets as well as the theory of harmonic spaces. All these theories have roots in classical potential theory. The theory of harmonic spaces, sometimes also called axiomatic theory of harmonic functions, plays a particular role among the above mentioned theories. On the one hand, this theory has particularly close connections with classical potential theory. Its main notion is that of a harmonic function and its main aim is the generalization and unification of classical results and methods for application to an extended class of elliptic and parabolic second order partial differential equations. On the other hand, the theory of harmonic spaces is closely related to the theory of Markov processes. In fact, all important notions and results of the theory have a probabilistic interpretation.

Function Spaces and Potential Theory

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Release : 1999-11-22
Genre : Mathematics
Kind : eBook
Book Rating : 608/5 ( reviews)

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Book Synopsis Function Spaces and Potential Theory by : David R. Adams

Download or read book Function Spaces and Potential Theory written by David R. Adams. This book was released on 1999-11-22. Available in PDF, EPUB and Kindle. Book excerpt: "..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society

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