We study maximum principles for a class of linear, degenerate elliptic differential operators of the second order. The Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypotheses on the principal part and on the degeneracy set of the operator. We prove a Poincaré inequality, which then allows to define the functional setting where to study weak solutions for equations and inequalities involving this class of operators. A good example of such an operator is the Grushin operator, to which we devote particular attention. As an application of these tools in the degenerate elliptic setting, we prove a partial symmetry result for classical solutions of semilinear problems on bounded, symmetric and suitably convex domains and a nonexistence result for classical solutions of semilinear equations with subcritical growth defined on the whole space. We use here the method of moving planes, implemented just in the directions parallel to the degeneracy set of the Grushin operator.

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Dario Monticelli completed his Ph.D. in Mathematics in 2007 at the Università degli Studi in Milano, under the supervision of Prof. Kevin Payne. His research interests involve nonlinear analysis and calculus of variations, partial differential equations and inequalities involving elliptic and degenerate elliptic operators and maximum principles.

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**Book Description **Book Condition: New. Publisher/Verlag: LAP Lambert Academic Publishing | for a Class of Degenerate Elliptic Linear Operators | We study maximum principles for a class of linear, degenerate elliptic differential operators of the second order. The Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypotheses on the principal part and on the degeneracy set of the operator. We prove a Poincaré inequality, which then allows to define the functional setting where to study weak solutions for equations and inequalities involving this class of operators. A good example of such an operator is the Grushin operator, to which we devote particular attention. As an application of these tools in the degenerate elliptic setting, we prove a partial symmetry result for classical solutions of semilinear problems on bounded, symmetric and suitably convex domains and a nonexistence result for classical solutions of semilinear equations with subcritical growth defined on the whole space. We use here the method of moving planes, implemented just in the directions parallel to the degeneracy set of the Grushin operator. | Format: Paperback | Language/Sprache: english | 92 pp. Bookseller Inventory # K9783838389301

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**Book Description **LAP Lambert Acad. Publ. Aug 2010, 2010. Taschenbuch. Book Condition: Neu. Neuware - We study maximum principles for a class of linear, degenerate elliptic differential operators of the second order. The Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypotheses on the principal part and on the degeneracy set of the operator. We prove a Poincaré inequality, which then allows to define the functional setting where to study weak solutions for equations and inequalities involving this class of operators. A good example of such an operator is the Grushin operator, to which we devote particular attention. As an application of these tools in the degenerate elliptic setting, we prove a partial symmetry result for classical solutions of semilinear problems on bounded, symmetric and suitably convex domains and a nonexistence result for classical solutions of semilinear equations with subcritical growth defined on the whole space. We use here the method of moving planes, implemented just in the directions parallel to the degeneracy set of the Grushin operator. 92 pp. Englisch. Bookseller Inventory # 9783838389301

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**Book Description **LAP Lambert Acad. Publ. Aug 2010, 2010. Taschenbuch. Book Condition: Neu. Neuware - We study maximum principles for a class of linear, degenerate elliptic differential operators of the second order. The Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypotheses on the principal part and on the degeneracy set of the operator. We prove a Poincaré inequality, which then allows to define the functional setting where to study weak solutions for equations and inequalities involving this class of operators. A good example of such an operator is the Grushin operator, to which we devote particular attention. As an application of these tools in the degenerate elliptic setting, we prove a partial symmetry result for classical solutions of semilinear problems on bounded, symmetric and suitably convex domains and a nonexistence result for classical solutions of semilinear equations with subcritical growth defined on the whole space. We use here the method of moving planes, implemented just in the directions parallel to the degeneracy set of the Grushin operator. 92 pp. Englisch. Bookseller Inventory # 9783838389301

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**Book Description **LAP Lambert Academic Publishing. Paperback. Book Condition: New. Paperback. 92 pages. Dimensions: 8.7in. x 5.9in. x 0.2in.We study maximum principles for a class of linear, degenerate elliptic differential operators of the second order. The Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypotheses on the principal part and on the degeneracy set of the operator. We prove a Poincar inequality, which then allows to define the functional setting where to study weak solutions for equations and inequalities involving this class of operators. A good example of such an operator is the Grushin operator, to which we devote particular attention. As an application of these tools in the degenerate elliptic setting, we prove a partial symmetry result for classical solutions of semilinear problems on bounded, symmetric and suitably convex domains and a nonexistence result for classical solutions of semilinear equations with subcritical growth defined on the whole space. We use here the method of moving planes, implemented just in the directions parallel to the degeneracy set of the Grushin operator. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Bookseller Inventory # 9783838389301

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**Book Description **LAP Lambert Academic Publishing, Germany, 2010. Paperback. Book Condition: New. Language: English . Brand New Book. We study maximum principles for a class of linear, degenerate elliptic differential operators of the second order. The Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypotheses on the principal part and on the degeneracy set of the operator. We prove a Poincar inequality, which then allows to define the functional setting where to study weak solutions for equations and inequalities involving this class of operators. A good example of such an operator is the Grushin operator, to which we devote particular attention. As an application of these tools in the degenerate elliptic setting, we prove a partial symmetry result for classical solutions of semilinear problems on bounded, symmetric and suitably convex domains and a nonexistence result for classical solutions of semilinear equations with subcritical growth defined on the whole space. We use here the method of moving planes, implemented just in the directions parallel to the degeneracy set of the Grushin operator. Bookseller Inventory # KNV9783838389301

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**Book Description **LAP Lambert Acad. Publ. Aug 2010, 2010. Taschenbuch. Book Condition: Neu. This item is printed on demand - Print on Demand Neuware - We study maximum principles for a class of linear, degenerate elliptic differential operators of the second order. The Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypotheses on the principal part and on the degeneracy set of the operator. We prove a Poincaré inequality, which then allows to define the functional setting where to study weak solutions for equations and inequalities involving this class of operators. A good example of such an operator is the Grushin operator, to which we devote particular attention. As an application of these tools in the degenerate elliptic setting, we prove a partial symmetry result for classical solutions of semilinear problems on bounded, symmetric and suitably convex domains and a nonexistence result for classical solutions of semilinear equations with subcritical growth defined on the whole space. We use here the method of moving planes, implemented just in the directions parallel to the degeneracy set of the Grushin operator. 92 pp. Englisch. Bookseller Inventory # 9783838389301

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