TY - GEN A1 - Sauvigny, Friedrich T1 - Surfaces of prescribed mean curvature H(x,y,z) with one-to-one central projection onto a plane T2 - Pacific Journal of Mathematics KW - Surfaces of prescribed mean curvature Y1 - 2016 UR - http://msp.org/pjm/2016/281-2/index.xhtml U6 - https://doi.org/10.2140/pjm.2016.281.481 SN - 0030-8730 VL - 281 IS - 2 SP - 481 EP - 509 ER - TY - BOOK A1 - Künnemann, Andreas T1 - Lösbarkeit von Randwertproblemen mittels komplexer Integralgleichungen KW - Differentialgleichungen im Komplexen Y1 - 2016 SN - 978-3-658-13126-5 SN - 978-3-658-13125-8 PB - Springer Spektrum CY - Wiesbaden ER - TY - GEN A1 - Sauvigny, Friedrich T1 - Maximum Principle for H-Surfaces in the Unit Cone and Dirichlet’s Problem for their Equation in Central Projection T2 - Milan Journal of Mathematics KW - Maximum principle KW - H-surfaces in cones Y1 - 2016 UR - http://link.springer.com/article/10.1007/s00032-016-0250-9 U6 - https://doi.org/10.1007/s00032-016-0250-9 SN - 1424-9286 VL - 84 IS - 1 SP - 91 EP - 104 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - Multiple solutions for the nonparametric Plateau problem within the Euclidean space Rᴾ of arbitrary dimension T2 - Calculus of Variations and Partial Differential Equations Y1 - 2016 UR - http://link.springer.com/article/10.1007/s00526-016-1087-3 U6 - https://doi.org/10.1007/s00526-016-1087-3 SN - 0944-2669 SN - 1432-0835 VL - 55 IS - 6, Artikel 140 SP - 1 EP - 28 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - Solution of boundary value problems for surfaces of prescribed mean curvature H (x, y, z) with 1–1 central projection via the continuity method T2 - Lithuanian mathematical journal N2 - 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. Radó 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. Y1 - 2018 U6 - https://doi.org/10.1007/s10986-018-9399-y SN - 1573-8825 SN - 0363-1672 VL - 58 IS - 3 SP - 320 EP - 328 ER - TY - BOOK A1 - Sauvigny, Friedrich T1 - Spektraltheorie selbstadjungierter Operatoren im Hilbertraum und elliptischer Differentialoperatoren Y1 - 2019 SN - 978-3-662-58069-1 SN - 978-3-662-58068-4 U6 - https://doi.org/10.1007/978-3-662-58069-1 PB - Springer Spektrum CY - Heidelberg [u.a] ER - TY - JOUR A1 - Hauer, Daniel A1 - He, Yuhan A1 - Liu, Dehui T1 - Fractional Powers of Monotone Operators in Hilbert Spaces JF - Advanced Nonlinear Studies N2 - The aim of this article is to provide a functional analytical framework for defining the fractional powers As for −1 < s < 1 of maximal monotone (possibly multivalued and nonlinear) operators A in Hilbert spaces.We investigate the semigroup {e−As t}t≥0 generated by −As, prove comparison principles and interpolations properties of {e−As t}t≥0 in Lebesgue and Orlicz spaces. We give sufficient conditions implying that As has a sub-differential structure. These results extend earlier ones obtained in the case s = 1/2 for maximal monotone operators [H. Brézis, Équations d’évolution du second ordre associées à des opérateurs monotones, Israel J. Math. 12 (1972), 51–60], [V. Barbu, A class of boundary problems for second order abstract differential equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 19 (1972), 295–319], [V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff international, Leiden, 1976], [E. I. Poffald and S. Reich, An incomplete Cauchy problem, J. Math. Anal. Appl. 113 (1986), no. 2, 514–543], and the recent advances for linear operators A obtained in [L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations 32 (2007), no. 7–9, 1245–1260], [P. R. Stinga and J. L. Torrea, Extension problem and Harnack’s inequality for some fractional operators, Comm. Partial Differential Equations 35 (2010), no. 11, 2092–2122]. Y1 - 2019 U6 - https://doi.org/10.1515/ans-2019-2053 SN - 1536-1365 VL - 19 IS - 4 SP - 717 EP - 755 PB - Walter de Gruyter GmbH ER - TY - JOUR A1 - Hauer, Daniel A1 - Mazón, José M. T1 - Kurdyka–Łojasiewicz–Simon inequality for gradient flows in metric spaces JF - Transactions of the American Mathematical Society Y1 - 2019 U6 - https://doi.org/10.1090/tran/7801 SN - 0002-9947 VL - 372 IS - 7 SP - 4917 EP - 4976 PB - American Mathematical Society (AMS) ER - TY - JOUR A1 - Chill, Ralph A1 - Hauer, Daniel A1 - Kennedy, James T1 - Nonlinear semigroups generated by j-elliptic functionals JF - Journal de Mathématiques Pures et Appliquées Y1 - 2016 U6 - https://doi.org/10.1016/j.matpur.2015.11.005 SN - 0021-7824 VL - 105 IS - 3 SP - 415 EP - 450 PB - Elsevier BV ER - TY - JOUR A1 - Goldstein, Jerome A. A1 - Hauer, Daniel A1 - Rhandi, Abdelaziz T1 - Existence and nonexistence of positive solutions of p-Kolmogorov equations perturbed by a Hardy potential JF - Nonlinear Analysis Y1 - 2016 U6 - https://doi.org/10.1016/j.na.2015.07.016 SN - 0362-546X VL - 131 SP - 121 EP - 154 PB - Elsevier BV ER - TY - JOUR A1 - Hauer, Daniel T1 - The p-Dirichlet-to-Neumann operator with applications to elliptic and parabolic problems JF - Journal of Differential Equations Y1 - 2015 U6 - https://doi.org/10.1016/j.jde.2015.04.030 SN - 0022-0396 VL - 259 IS - 8 SP - 3615 EP - 3655 PB - Elsevier BV ER - TY - JOUR A1 - Dancer, E.N. A1 - Daners, Daniel A1 - Hauer, Daniel T1 - Uniform convergence of solutions to elliptic equations on domains with shrinking holes JF - Advances in Differential Equations Y1 - 2015 U6 - https://doi.org/10.57262/ade/1427744013 SN - 1079-9389 VL - 20 IS - 5/6 SP - 463 EP - 494 PB - Khayyam Publishing, Inc ER -