TY - GEN A1 - Sauvigny, Friedrich A1 - Schulz, Friedmar A1 - Ströhmer, Gerhard A1 - Friedrich, Tomi T1 - Professor Heinz on the occasion of his 85th birthday Y1 - 2009 ER - TY - CHAP A1 - Sauvigny, Friedrich T1 - Global C hoch (2+alpha)- estimates for conformal maps T2 - Geometric analysis and nonlinear partial differential equations KW - conformal mappinga priori estimates Y1 - 2003 SN - 978-3-540-44051-2 SN - 3-540-44051-8 SP - 105 EP - 115 PB - Springer CY - Berlin [u.a.] ET - 1. Auflage ER - TY - BOOK A1 - Sauvigny, Friedrich T1 - Partielle Differentialgleichungen der Geometrie und der Physik 1 - Grundlagen und Integraldarstellungen : unter Berücksichtigung der Vorlesungen von E. Heinz N2 - Dieses zweibändige Lehrbuch stellt das Gesamtgebiet der partiellen Differentialgleichungen - vom elliptischen, parabolischen und hyperbolischen Typ - in zwei und mehreren Veränderlichen vor. In diesem Band werden die Differentialgleichungen mit Integraldarstellungen behandelt, während im nächsten Band funktionalanalytische Lösungsmethoden vorgestellt werden. KW - Partielle Differentialgleichungen KW - Funktionentheorie KW - Funktionalanalysis Y1 - 2004 SN - 3-540-20453-9 PB - Springer CY - Berlin [u.a.] ER - TY - BOOK A1 - Sauvigny, Friedrich T1 - Partielle Differentialgleichungen der Geometrie und der Physik 2 - Funktionalanalytische Lösungsmethoden : unter Berücksichtigung der Vorlesungen von E. Heinz N2 - Dieses zweibändige Lehrbuch stellt das Gesamtgebiet der partiellen Differentialgleichungen - vom elliptischen, parabolischen und hyperbolischen Typ - in zwei und mehreren Veränderlichen vor.Während im ersten Band Integraldarstellungen im Mittelpunkt standen, werden in diesem Band funktionalanalytische Lösungsmethoden vorgestellt. KW - Partielle Differentialgleichungen KW - Funktionentheorie KW - Funktionalanalysis KW - Differentialgeometrie Y1 - 2005 SN - 3-540-23107-2 PB - Springer CY - Berlin [u.a.] ER - TY - JOUR A1 - Sauvigny, Friedrich T1 - Über nichtlineare elliptische Differentialgleichungssysteme Y1 - 2004 ER - TY - JOUR A1 - Sauvigny, Friedrich T1 - Deformation of boundary value problems for surfaces with prescribed mean curvature Y1 - 2001 ER - TY - JOUR A1 - Sauvigny, Friedrich T1 - Introduction of isothermal parameters into a Riemannian metric by the continuity method Y1 - 1999 ER - TY - JOUR A1 - Sauvigny, Friedrich A1 - Hildebrandt, Stefan T1 - Minimal surfaces in a wedge III. Existence of graph solutions and some uniqueness results Y1 - 1999 ER - TY - GEN A1 - Sauvigny, Friedrich A1 - Hildebrandt, Stefan T1 - Minimal surfaces in a wedge IV. Hölder estimates of the Gauss map and a Bernstein theorem T2 - Calculus of Variations and Partial Differential Equations Y1 - 1999 SN - 0944-2669 SN - 1432-0835 VL - 8 IS - 1 SP - 71 EP - 90 ER - TY - JOUR A1 - Sauvigny, Friedrich A1 - Hildebrandt, Stefan T1 - Minimal surfaces in a wedge II. The edge-creeping phenomenon Y1 - 1997 ER - TY - JOUR A1 - Sauvigny, Friedrich A1 - Hildebrandt, Stefan T1 - Minimal surfaces in a wedge I. Asymptotic expansions Y1 - 1997 ER - TY - BOOK A1 - Sauvigny, Friedrich T1 - Partial Differential Equations 1 - Foundations and Integral Representations N2 - Integration and differentiation on manifolds, Functional analytic foundations, Brouwer's degree of mapping, Generalized analytic functions, Potential theory and spherical harmonics, Linear partial differential equations Y1 - 2006 SN - 3-540-34457-8 PB - Springer CY - Berlin [u.a.] ER - TY - BOOK A1 - Sauvigny, Friedrich T1 - Partial Differential Equations 2 - Functional Analytic Methods Y1 - 2012 SN - 978-7-5100-3516-6 PB - World Publishing Corporation Beijing Company CY - Beijing, China ER - TY - GEN A1 - Sauvigny, Friedrich A1 - Hildebrandt, Stefan T1 - Relative minimizers of energy are relative minimizers of area Y1 - 2010 ER - TY - BOOK A1 - Sauvigny, Friedrich A1 - Dierkes, Ulrich A1 - Hildebrandt, Stefan T1 - Minimal Surfaces Y1 - 2010 SN - 978-3-642-11715-2 PB - Springer CY - Berlin ET - 2. rev. ed ER - TY - GEN A1 - Sauvigny, Friedrich T1 - Un problème aux limites mixte des surfaces minimales avec une multiple projection plane et le dessin optimal des escaliers tournants Y1 - 2010 ER - TY - GEN A1 - Sauvigny, Friedrich A1 - Hildebrandt, Stefan T1 - An energy estimate for the difference of solutions for the n-dimensional solution with prescribed mean curvature and removable singularities Y1 - 2009 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - Mixed Boundary Value Problems for Minimal Graphs on a Riemann Surface and Winding Staircases Y1 - 2011 ER - TY - BOOK A1 - Sauvigny, Friedrich T1 - Partial Differential Equations 1 - Foundations and Integral Representations Y1 - 2012 SN - 978-7-5100-3517-3 PB - World Publishing Corporation Beijing Company CY - Beijing, China ER - TY - BOOK A1 - Sauvigny, Friedrich T1 - Partial Differential Equations 2 - Functional Analytic Methods Y1 - 2006 SN - 3-540-34461-6 PB - Springer CY - Berlin [u.a.] ER - TY - BOOK A1 - Sauvigny, Friedrich T1 - Partial Differential Equations 1 - Foundations and Integral Representations Y1 - 2012 SN - 978-1-4471-2980-6 PB - Springer CY - London ET - 2. ed. ER - TY - BOOK A1 - Sauvigny, Friedrich T1 - Partial Differential Equations 2 - Functional Analytic Methods Y1 - 2012 SN - 978-1-447-12983-7 PB - Springer CY - London ET - 2. ed. ER - TY - THES A1 - Sauvigny, Friedrich T1 - Flächen vorgeschriebener mittlerer Krümmung mit eineindeutiger Projektion auf eine Ebene N2 - Dissertation an der Mathematisch-Naturwissenschaftlichen Fakultät der Georg-August-Universität Göttingen. Y1 - 1981 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - Flächen vorgeschriebener mittlerer Krümmung mit eineindeutiger Projektion auf eine Ebene T2 - Mathematische Zeitschrift Y1 - 1982 SN - 0025-5874 VL - 180 IS - 1 SP - 41 EP - 67 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - On the total number of branch points of quasi-minimal surfaces bounded by a polygon T2 - Analysis Y1 - 1988 SN - 0174-4747 VL - 8 SP - 297 EP - 304 ER - TY - THES A1 - Sauvigny, Friedrich T1 - A-Priori-Abschätzungen der Hauptkrümmungen für Immersionen vom Mittleren-Krümmungs-Typ mittels Uniformisierung und Sätze vom Bernstein-Typ N2 - Habilitationsschrift am Fachbereich Mathematik an der Georg-August-Universität Göttingen. Y1 - 1989 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - On immersions of constant mean curvature: Compactness results and finiteness theorems for Plateau's problem T2 - Archive for Rational Mechanics and Analysis Y1 - 1990 SN - 0003-9527 VL - 110 IS - 2 SP - 125 EP - 140 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - Curvature estimates for immersions of minimal surface type via uniformization and theorems of Bernstein type T2 - Manuscripta Mathematica Y1 - 1990 SN - 0025-2611 VL - 67 SP - 69 EP - 97 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - A priori estimates of the principal curvatures for immersions of prescribed mean curvature and theorems of Bernstein type T2 - Mathematische Zeitschrift Y1 - 1990 SN - 0025-5874 VL - 205 IS - 1 SP - 567 EP - 582 ER - TY - GEN A1 - Sauvigny, Friedrich A1 - Hildebrandt, Stefan T1 - Embeddedness and uniqueness of minimal surfaces solving a partially free boundary value problem T2 - Journal für die reine und angewandte Mathematik Y1 - 1991 SN - 0075-4102 VL - 422 SP - 69 EP - 89 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - A new proof of the gradient estimate for graphs of prescribed mean curvature T2 - Manuscripta mathematica Y1 - 1992 SN - 0025-2611 VL - 74 IS - 1 SP - 83 EP - 86 ER - TY - GEN A1 - Sauvigny, Friedrich A1 - Hildebrandt, Stefan T1 - On one-to-one harmonic mappings and minimal surfaces T2 - Nachrichten der Akademie der Wissenschaften zu Göttingen, 2. Mathematisch-Physikalische Klasse Y1 - 1992 SN - 0065-5295 IS - 3 SP - 73 EP - 93 ER - TY - GEN A1 - Sauvigny, Friedrich A1 - Hildebrandt, Stefan T1 - Uniqueness of stable minimal surfaces with partially free boundaries T2 - Journal of the Mathematical Society of Japan Y1 - 1995 SN - 0025-5645 VL - 47 IS - 3 SP - 423 EP - 440 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - Die zweite Variation von Minimalflächen im R-hoch-p mit polygonalem Rand T2 - Mathematische Zeitschrift Y1 - 1985 SN - 0025-5874 VL - 189 SP - 167 EP - 184 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - Ein Eindeutigkeitssatz für Minimalflächen im R-hoch-p mit polygonalem Rand T2 - Journal für die reine und angewandte Mathematik Y1 - 1985 SN - 0075-4102 VL - 358 SP - 92 EP - 96 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - On the Morse index of minimal surfaces in R-hoch-p with polygonal boundaries T2 - Manuscripta Mathematica Y1 - 1985 SN - 0025-2611 VL - 53 SP - 167 EP - 197 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - Über das Plateausche Problem für Wendelkurven T2 - Mathematische Semesterberichte Y1 - 2013 SN - 0720-728X SN - 1432-1815 VL - 60 IS - 2 SP - 151 EP - 183 ER - TY - BOOK A1 - Sauvigny, Friedrich T1 - Analysis : Grundlagen, Differentiation, Integrationstheorie, Differentialgleichungen, Variationsmethoden Y1 - 2014 SN - 978-3-642-41506-7 SN - 978-3-642-41507-4 PB - Springer Spektrum CY - Berlin [u.a.] ER - TY - CHAP A1 - Hildebrandt, Stefan A1 - Sauvigny, Friedrich ED - Apushkinskaya, Darya ED - Nazarov, Alexander I. T1 - On Plateaus's problem in Riemannian manifolds T2 - Proceedings of the St. Petersburg mathematical society : advances in mathematical analysis of partial differential equations ; dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya Y1 - 2014 SN - 978-1-4704-1551-8 SP - 141 EP - 152 PB - American Mathematical Soc. CY - Providence, RI ER - 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 - 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 - BOOK A1 - Sauvigny, Friedrich T1 - Analysis BT - Grundlagen, Differentiation, Integrationstheorie, Differentialgleichungen, Variationsmethoden, Funktionenräume, Darstellungssätze Y1 - 2024 SN - 978-3-662-69864-8 U6 - https://doi.org/10.1007/978-3-662-69865-5 PB - Springer Berlin Heidelberg CY - Berlin, Heidelberg ET - 2 ER - TY - GEN A1 - Sauvigny, Friedrich T1 - Minimal graphs in Riemannian spaces T2 - Calculus of Variations and Partial Differential Equations Y1 - 2024 U6 - https://doi.org/10.1007/s00526-024-02704-w SN - 1432-0835 SN - 0944-2669 VL - 63 IS - 5 SP - 1 EP - 47 ER -