Anisotropic p-Laplacian equations: new approaches to the theory of regularit

Anisotropic p-Laplacian equations: new approaches to the theory of regularit

online

2022-01-12 - 17:00

Simone Ciani

Technische Universität Darmstadt

Fachbereich Mathematik, Schlossgartenstrasse 7, 64289 Germany.

In this brief talk we will introduce an equation in divergence form whose principal part is the Euler-Lagrange equation of the energy integral

F(u)=Ni=11piΩ|iu|pidx,Ω⊂⊂RN,

known to be the prototype of orthotropic non-standard growth functionals F in Calculus of Variations. We will focus on the similarities and differences of the theory of regularity in comparison with the p-Laplacian one, and describe a problem which is still active and widely open after more than fifty years.

We will show why a new approach to the theory of regularity concerning these general functionals is required, and present some possible new methods, adapted from parabolic differential equations.

Key Words: Anisotropic p-Laplacian, degenerate and singular equations, parabolic and elliptic equations.

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