Inverse problems for elliptic equations with power type nonlinearities

Inverse problems for elliptic equations with power type nonlinearities

Matti Lassas Department of Mathematics and Statistics, University of Helsinki matti.lassas@helsinki.fi Tony Liimatainen Department of Mathematics and Statistics, University of Jyväskylä tony.liimatainen@helsinki.fi Yi-Hsuan Lin Department of Mathematics and Statistics, University of Jyväskylä yihsuanlin3@gmail.com  and  Mikko Salo Department of Mathematics and Statistics, University of Jyväskylä mikko.j.salo@jyu.fi
Abstract.

We introduce a method for solving Calderón type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. Assuming the knowledge of a nonlinear Dirichlet-to-Neumann map, we determine both a potential and a conformal manifold simultaneously in dimension , and a potential on transversally anisotropic manifolds in dimensions . In the Euclidean case, we show that one can solve the Calderón problem for certain semilinear equations in a surprisingly simple way without using complex geometrical optics solutions.

Keywords. Inverse boundary value problem, Calderón problem, semilinear equation, Riemannian manifold, transversally anisotropic.

Contents

1. Introduction

Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
""
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
   
Add comment
Cancel
Loading ...
363512
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description