Hugo Tavares - Topics in elliptic problems: from semilinear equations to shape optimization

cm:12568 - Communications in Mathematics, March 14, 2024, Volume 32 (2024), Issue 3 (Special issue: Portuguese Mathematics) - https://doi.org/10.46298/cm.12568
Topics in elliptic problems: from semilinear equations to shape optimizationArticle

Authors: Hugo Tavares

    In this paper, which corresponds to an updated version of the author's Habilitation lecture in Mathematics, we do an overview of several topics in elliptic problems. We review some old and new results regarding the Lane-Emden equation, both under Dirichlet and Neumann boundary conditions, then focus on sign-changing solutions for Lane-Emden systems. We also survey some results regarding fully nontrivial solutions to gradient elliptic systems with mixed cooperative and competitive interactions. We conclude by exhibiting results on optimal partition problems, with cost functions either related to Dirichlet eigenvalues or to the Yamabe equation. Several open problems are referred along the text.


    Volume: Volume 32 (2024), Issue 3 (Special issue: Portuguese Mathematics)
    Published on: March 14, 2024
    Accepted on: January 21, 2024
    Submitted on: November 18, 2023
    Keywords: Mathematics - Analysis of PDEs,35B09, 35B33, 35B38, 35B45, 35B65, 35J20, 35J50, 35J61, 35R35, 49Q05, 58J05, 58E05

    Consultation statistics

    This page has been seen 112 times.
    This article's PDF has been downloaded 61 times.