Skip to main content

A Priori Estimates

  • 1202 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1499)

Abstract

This Chapter 6 and the next Chapter 7 are devoted to the proof of Theorem 1.2. In this chapter we study the operator Ap, and prove a priori estimates for the operator Ap − λI (Theorem 6.3) which will play a fundamental role in the next chapter. In the proof we make good use of Agmon’s method (Proposition 6.4). This is a technique of treating a spectral parameter λ as a second-order, elliptic differential operator of an extra variable and relating the old problem to a new problem with the additional variable

Keywords

  • Partial Differential Equation
  • Positive Constant
  • Linear Operator
  • Differential Operator
  • Markov Process

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kazuaki Taira .

Rights and permissions

Reprints and Permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Taira, K. (2009). A Priori Estimates. In: Boundary Value Problems and Markov Processes. Lecture Notes in Mathematics(), vol 1499. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01677-6_6

Download citation