How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

2. Complete and sign the license agreement.

3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2213  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046
Email: cust-serv@ams.org

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

memo_has_moved_text();Fundamental solutions and local solvability for nonsmooth Hörmander’s operators

About this Title

Marco Bramanti, Luca Brandolini, Maria Manfredini and Marco Pedroni

Publication: Memoirs of the American Mathematical Society
Publication Year: 2017; Volume 249, Number 1182
ISBNs: 978-1-4704-2559-3 (print); 978-1-4704-4131-9 (online)
DOI: https://doi.org/10.1090/memo/1182
Published electronically: August 8, 2017
Keywords:Nonsmooth Hörmander’s vector fields, fundamental solution, solvability, Hölder estimates.

View full volume PDF

View other years and numbers:

Table of Contents

Chapters

• Chapter 1. Introduction
• Chapter 2. Some known results about nonsmooth Hörmander’s vector fields ec known results
• Chapter 3. Geometric estimatesec geometric
• Chapter 4. The parametrix methodec parametrix
• Chapter 5. Further regularity of the fundamental solution and local solvability of $L$
• Chapter 6. Appendix. Examples of nonsmooth Hörmander’s operators satisfying assumptions A or B

Abstract

We consider operators of the form in a bounded domain of where are nonsmooth Hörmander's vector fields of step such that the highest order commutators are only Hölder continuous. Applying Levi's parametrix method we construct a local fundamental solution for and provide growth estimates for and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients we prove that also possesses second derivatives, and we deduce the local solvability of , constructing, by means of , a solution to with Hölder continuous . We also prove estimates on this solution.