Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation
- ISBN-10
- 0821835092
- ISBN-13
- 9780821835098
- Category
- Science
- Pages
- 121
- Language
- English
- Published
- 2004
- Publisher
- American Mathematical Soc.
- Author
- Benoît Mselati
Description
We are concerned with the nonnegative solutions of $\Delta u = u^2$ in a bounded and smooth domain in $\mathbb{R}^d$. We prove that they are uniquely determined by their fine trace on the boundary as defined in [DK98a], thus answering a major open question of [Dy02]. A probabilistic formula for a solution in terms of its fine trace and of the Brownian snake is also provided. A major role is played by the solutions which are dominated by a harmonic function in $D$. The latters are called moderate in Dynkin's terminology. We show that every nonnegative solution of $\Delta u = u^2$ in $D$ is the increasing limit of moderate solutions.
Get the book
Similar books
-
Chemistry: An Introduction to General, Organic and Biological Chemistry
By Karen C. TimberlakeThis new edition introduces more problem-solving strategies and new conceptual and challenge problems. Also, each Chapter Review has been enhanced with Learning Goals to reinforce the mastery of concepts for students.
-
Chemistry: An Introduction to General, Organic, and Biological Chemistry
By Karen TimberlakeThis laboratory manual contains 42 experiments for the standard sequence of topics in general, organic, and biological chemistry.
-
Basic Chemistry
By Karen C. TimberlakeThe book guides students through basic chemistry problem solving with engaging visuals and a focus on developing the math skills necessary to be successful in the course.
-
General, Organic, and Biological Chemistry: Structures of Life, eBook, Global Edition
By Karen C. TimberlakeThe full text downloaded to your computer With eBooks you can: search for key concepts, words and phrases make highlights and notes as you study share your notes with friends eBooks are downloaded to your computer and accessible either ...
-
Basic Chemistry
By Karen C. Timberlake, William E. TimberlakeBasic Chemistry
-
Basic Chemistry, Books a la Carte Edition
By Karen C. TimberlakeBasic Chemistry, Books a la Carte Edition
-
Essential Laboratory Manual for General, Organic and Biological Chemistry
By Karen C. TimberlakeEssential Laboratory Manual for General, Organic and Biological Chemistry
-
Basic Chemistry, Global Edition
By Karen C. Timberlake, Bill TimberlakeThe main objective in writing this text is to make the study of chemistry an engaging and a positive experience for students by relating the structure and behaviour of matter to real life.
-
General, Organic, and Biological Chemistry: An Integrated Approach
By Karen C. Timberlake, Laura D. Frost, Todd S. DealThe eText pages look exactly like the printed text, and include powerful interactive and customization functions. This is the product access code card for MasteringChemistry with Pearson eText and does not include the actual bound book.
-
Chemistry: An Introduction to General, Organic, and Biological Chemistry
By Karen C. TimberlakeHealth, Environmental, and Green Chemistry Notes throughout the text relate chemistry chapters to real-life topics in health, the environment, and medicine that are interesting and motivating to students.