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Sem. Równań Fiz. Mat.


Stability of solutions to elliptic PDEs under Musielak-Orlicz growth

Prelegent: Arttu Karppinen

2022-05-05 12:30

We investigate stability of solutions to elliptic nonlinear partial differential equations -div(A_i(x,Du))=0 when the growth rate of the differential operator A_i varies. A model example would be to consider solutions of p_i-Laplace equations with p_i converging to some p. Our framework considers Musielak-Orlicz functions so our results cover as special cases p-Laplace equation, p(x)-Laplace equation, Orlicz-Laplace equations and double phase equations among others. We show under standard structural assumptions that if (A_i) converges locally uniformly to A, then the corresponding sequence of A_i-harmonic functions (u_i) has a subsequence converging to the A-harmonic function u in Sobolev and Hoelder spaces. The talk is based on joint work with Petteri Harjulehto [arXiv:2203.13624].



Meeting ID: 828 8178 3943
Passcode: 435791