Nonlinear Elliptic and Parabolic Problems: A Special Tribute to the Work of Herbert Amann (Progress in Nonlinear Differential Equations and Their ... Equations and Their Applications (64))

The Present Volume Is Dedicated To Celebrate The Work Of The Renowned Mathematician Herbert Amann, Who Had A Significant And Decisive Influence In Shaping Nonlinear Analysis. Most Articles Published In This Book, Which Consists Of 32 Articles In Total, Written By Highly Distinguished Researchers, Are In One Way Or Another Related To The Scientific Works Of Herbert Amann. The Contributions Cover A Wide Range Of Nonlinear Elliptic And Parabolic Equations With Applications To Natural Sciences And Engineering. Special Topics Are Fluid Dynamics, Reaction-diffusion Systems, Bifurcation Theory, Maximal Regularity, Evolution Equations, And The Theory Of Function Spaces. Bounded Imaginary Powers And H?-calculus Of The Stokes Operator In Unbounded Domains -- Exact Estimates Of Solutions To The Robin Boundary Value Problem For Elliptic Non-divergent Second-order Equations In A Neighborhood Of The Boundary Conical Point -- Well-posedness Of A Two-phase Flow With Soluble Surfactant -- Resolvent Differences For General Obstacles -- Special Finite Time Extinction In Nonlinear Evolution Systems: Dynamic Boundary Conditions And Coulomb Friction Type Problems -- Spectral Projections, Riesz Transforms And H?-calculus For Bisectorial Operators -- Very Weak Solutions Of Stationary And Instationary Navier-stokes Equations With Nonhomogeneous Data -- Grow-up On The Boundary For A Semilinear Parabolic Problem -- Existence And Uniqueness Results For Reaction-diffusion Processes Of Electrically Charged Species -- An Inverse Problem For A Phase-field Model In Sobolev Spaces -- Numerical Analysis Of Microstructures: The Influence Of Incompatibility --^ Nonlinear Singular Elliptic Problems: Recent Results And Open Problems -- The Navier-stokes Flow In The Exterior Of Rotating Obstacles -- A Global Bifurcation Result For Variational Inequalities -- On Elliptic Non-divergence Operators With Measurable Coefficients -- A Chemotaxis Model With Threshold Density And Degenerate Diffusion -- In The Blink Of An Eye -- Generalized Minimal Cardinal Of The ?-slices Of The Semi-bounded Components Arising In Global Bifurcation Theory -- Blow-up Of Solutions Of A Semilinear Heat Equation With A Visco-elastic Term -- Finite Element Methods For Investigating The Moving Boundary Problem In Biological Development -- Existence Of Weak Solutions To The Equations Of Stationary Motion Of Heat-conducting Incompressible Viscous Fluids -- Liouville Type Theorems And Complete Blow-up For Indefinite Superlinear Parabolic Equations -- On Reducing The 2d Navier-stokes Equations To A System Of Delayed Odes -- Quasilinear Parabolic Equations In Lp --^ Parabolic Equations In Locally Uniform Spaces -- Bifurcation Of Traveling Waves Related To The Bénard Equations With An Exterior Force -- Vector-valued Sobolev Spaces And Gagliardo-nirenberg Inequalities -- The Influence Of Gradient Perturbations On Blow-up Asymptotics In Semilinear Parabolic Problems: A Survey -- Non-existence Of Positive Solutions For Diffusive Logistic Equations With Nonlinear Boundary Conditions -- Extremal Equilibria And Asymptotic Behavior Of Parabolic Nonlinear Reaction-diffusion Equations -- A Remark On Continuous Coagulation-fragmentation Equations With Unbounded Diffusion Coefficients -- On Lp-estimates Of Optimal Type For The Parabolic Oblique Derivative Problem With Vmo-coefficients — A Refined Version. Michel Chipot, Joachim Escher, Editors. Includes Bibliographical References. Bounded Imaginary Powers and H ∞ -Calculus of the Stokes Operator in Unbounded Domains....Pages 1-15 Exact Estimates of Solutions to the Robin Boundary Value Problem for Elliptic Non-divergent Second-order Equations in a Neighborhood of the Boundary Conical Point....Pages 17-35 Well-posedness of a Two-phase Flow with Soluble Surfactant....Pages 37-61 Resolvent Differences for General Obstacles....Pages 63-70 Special Finite Time Extinction in Nonlinear Evolution Systems: Dynamic Boundary Conditions and Coulomb Friction Type Problems....Pages 71-97 Spectral Projections, Riesz Transforms and H ∞ -calculus for Bisectorial Operators....Pages 99-112 Very Weak Solutions of Stationary and Instationary Navier-Stokes Equations with Nonhomogeneous Data....Pages 113-136 Grow-up on the Boundary for a Semilinear Parabolic Problem....Pages 137-150 Existence and Uniqueness Results for Reaction-diffusion Processes of Electrically Charged Species....Pages 151-188 An Inverse Problem for a Phase-field Model in Sobolev Spaces....Pages 189-210 Numerical Analysis of Microstructures: The Influence of Incompatibility....Pages 211-225 Nonlinear Singular Elliptic Problems: Recent Results and Open Problems....Pages 227-242 The Navier-Stokes Flow in the Exterior of Rotating Obstacles....Pages 243-250 A Global Bifurcation Result for Variational Inequalities....Pages 253-264 On Elliptic Non-divergence Operators with Measurable Coefficients....Pages 265-272 A Chemotaxis Model with Threshold Density and Degenerate Diffusion....Pages 273-290 In the blink of an Eye....Pages 291-327 Generalized Minimal Cardinal of the λ-slices of the Semi-bounded Components Arising in Global Bifurcation Theory....Pages 329-349 Blow-up of Solutions of a Semilinear Heat Equation with a Visco-elastic Term....Pages 351-356 Finite Element Methods for Investigating the Moving Boundary Problem in Biological Development....Pages 357-371 Existence of Weak Solutions to the Equations of Stationary Motion of Heat-conducting Incompressible Viscous Fluids....Pages 373-390 Liouville Type Theorems and Complete Blow-up for Indefinite Superlinear Parabolic Equations....Pages 391-402 On Reducing the 2d Navier-Stokes Equations to a System of Delayed ODEs....Pages 403-411 Quasilinear Parabolic Equations in L p ....Pages 413-419 Parabolic Equations in Locally Uniform Spaces....Pages 421-432 Bifurcation of Traveling Waves Related to the Bénard Equations with an Exterior Force....Pages 433-462 Vector-valued Sobolev Spaces and Gagliardo-Nirenberg Inequalities....Pages 463-472 The Influence of Gradient Perturbations on Blow-up Asymptotics in Semilinear Parabolic Problems: A Survey....Pages 473-495 Non-existence of Positive Solutions for Diffusive Logistic Equations with Nonlinear Boundary Conditions....Pages 497-507 Extremal Equilibria and Asymptotic Behavior of Parabolic Nonlinear Reaction-diffusion Equations....Pages 509-516 A Remark on Continuous Coagulation-Fragmentation Equations with Unbounded Diffusion Coefficients....Pages 517-528 On L p -Estimates of Optimal Type for the Parabolic Oblique Derivative Problem with VMO-Coefficients — A Refined Version....Pages 529-536