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David Hruška


PhD student

Leipzig University

Leipzig, Germany


hruska@math.uni-leipzig.de

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Research


My PhD project belongs to the intersection of regularity theory of elliptic partial differential equations with Geometric Measure Theory. It studies regularity questions about a class of shape optimization problems close to the isoperimetric problem. The most prominent model from this class arises in the theory of ferrofluids instabilities. Its main features (compared to known works) are the saddle structure (no minimizers) and nonlinearity of the term capturing the magnetism.

Other interests

I am also interested in PDEs coming from continuum mechanics (and the corresponding numerical results/simulations) and real analysis.


Publications


  • Bulíček, M., Hruška, D. & Málek, J., On evolutionary problems with a-priori bounded gradients,
    Calc. Var. 62, 188 (2023), journal, arXiv.
  • Hruška, D., A note on directional Lipschitz continuity in the Euclidean plane,
    Real Anal. Exchange 46 (2) 441 - 450, 2021, journal, arXiv.