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math.AP2023
A small remark on Bernstein's theorem
Michael Bildhauer, Bernhard Farquhar, Martin Fuchs
We investigate splitting-type variational problems with some linear growth conditions. For balanced solutions of the associated Euler-Lagrange equation we receive a result analogou…
math.AP2023
Splitting-type variational problems with asymmetrical growth conditions
Michael Bildhauer, Martin Fuchs
Splitting-type variational problems \[ \int_Ω\sum_{i=1}^n f_i(\partial_i w) dx \to \min \] with superlinear growth conditions are studied by assuming \[ h_i(t) \leq f''_i(t) \leq H…