@misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Solution of boundary value problems for surfaces of prescribed mean curvature H (x, y, z) with 1-1 central projection via the continuity method}, series = {Lithuanian mathematical journal}, volume = {58}, journal = {Lithuanian mathematical journal}, number = {3}, issn = {1573-8825}, doi = {10.1007/s10986-018-9399-y}, pages = {320 -- 328}, abstract = {When we consider surfaces of prescribed mean curvature H with a one-to-one orthogonal projection onto a plane, we have to study the nonparametric H-surface equation. Now the H-surfaces with a one-to-one central projection onto a plane lead to an interesting elliptic differential equation, which has been discovered for the case H = 0 already by T. Rad{\´o} in 1932. We establish the uniqueness of the Dirichlet problem for this H-surface equation in central projection and develop an estimate for the maximal deviation of large H-surfaces from their boundary values, resembling an inequality by J. Serrin from 1969. We solve the Dirichlet problem for nonvanishing H with compact support via a nonlinear continuity method. Here we introduce conformal parameters into the surface and study the well-known H-surface system. Then we combine these investigations with a differential equation for its unit normal, which has been developed by the author for variable H in 1982. Furthermore, we construct large H-surfaces bounding extreme contours by an approximation. Here we only provide an overview on the relevant proofs; for the more detailed derivations of our results, we refer the readers to the author's investigations in the Pacific Journal of Mathematics and the Milan Journal of Mathematics.}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Spektraltheorie selbstadjungierter Operatoren im Hilbertraum und elliptischer Differentialoperatoren}, publisher = {Springer Spektrum}, address = {Heidelberg [u.a]}, isbn = {978-3-662-58069-1}, doi = {10.1007/978-3-662-58069-1}, pages = {xi, 259}, language = {de} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Analysis}, edition = {2}, publisher = {Springer Berlin Heidelberg}, address = {Berlin, Heidelberg}, isbn = {978-3-662-69864-8}, doi = {10.1007/978-3-662-69865-5}, pages = {625}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Minimal graphs in Riemannian spaces}, series = {Calculus of Variations and Partial Differential Equations}, volume = {63}, journal = {Calculus of Variations and Partial Differential Equations}, number = {5}, issn = {1432-0835}, doi = {10.1007/s00526-024-02704-w}, pages = {1 -- 47}, language = {en} }