Skip to main content

The Dirichlet Problem and Weak Solutions

  • Chapter
  • First Online:
Notes on the Stationary p-Laplace Equation

Part of the book series: SpringerBriefs in Mathematics ((BRIEFSMATH))

  • 1417 Accesses

Abstract

The natural starting point is a Dirichlet integral

$$I(u)=\int _{\Omega }|\nabla u|^pdx$$

with the exponent p, \(1<p<\infty \), in place of the usual 2.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

eBook
USD 18.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    “Was it Plato who made his arguments by telling a story with an obvious flaw, and allowing the listener to realize the error?”

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Peter Lindqvist .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Lindqvist, P. (2019). The Dirichlet Problem and Weak Solutions. In: Notes on the Stationary p-Laplace Equation. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-14501-9_2

Download citation

Publish with us

Policies and ethics