Artikel
Open Access
Preface for the special issue on “Geometric Partial Differential Equations and Applications”
-
Guozhen Lu
,
Xi-Nan Ma
Veröffentlicht/Copyright:
31. Dezember 2023
This special issue of “Geometric Partial Differential Equations and Applications” published in de Gruyter journal Advanced Nonlinear Studies (ANS) focusses on recent significant progress in areas connected to fully nonlinear partial differential equations, convex geometric analysis, geometric rigidity, minimal submanifolds, geometric inequalities, and complex geometric analysis, and related topics.
This special issue includes articles on a priori estimates for the Monge-Ampére-type equation, regularity in optimal transport, the exterior problem for the Monge-Ampére and complex degenerate k-Hessian equations, complex geometry, and Kähler-Einstein metrics. It also contains results on Minkowski-type problems for convex bodies, prescribed degenerate curvature measure problems, the classical geometric theory of extrinsic geometric flows of Euclidean hypersurfaces, Ricci flow, minimal surfaces, geometric inequalities and rigidity, the classification of constant mean curvature surfaces of finite index, the capillary problem, and compactness with pinching for hypersurfaces.
In this special issue, we invited articles from both well-established mathematicians and young scholars. Many of them are leading researchers in the areas of geometric partial differential equations, differential geometry, and convex geometry. We are grateful to all the contributors and reviewers for making this special issue possible.
Advanced nonlinear studies (ANS) was founded as a traditional journal in 2001. It publishes cutting-edge original research on nonlinear problems, particularly those involving partial differential equations, calculus of variations, geometric analysis, nonlinear analysis and related topics. We are confident that this special issue contributes to strengthening and broadening the scope of this journal.
Published Online: 2023-12-31
© 2023 the author(s), published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.
Artikel in diesem Heft
- Research Articles
- Asymptotic properties of critical points for subcritical Trudinger-Moser functional
- The existence of positive solution for an elliptic problem with critical growth and logarithmic perturbation
- On some dense sets in the space of dynamical systems
- Sharp profiles for diffusive logistic equation with spatial heterogeneity
- Generic properties of the Rabinowitz unbounded continuum
- Global bifurcation of coexistence states for a prey-predator model with prey-taxis/predator-taxis
- Multiple solutions of p-fractional Schrödinger-Choquard-Kirchhoff equations with Hardy-Littlewood-Sobolev critical exponents
- Improved fractional Trudinger-Moser inequalities on bounded intervals and the existence of their extremals
- The existence of infinitely many boundary blow-up solutions to the p-k-Hessian equation
- A priori bounds, existence, and uniqueness of smooth solutions to an anisotropic Lp Minkowski problem for log-concave measure
- Existence of nonminimal solutions to an inhomogeneous elliptic equation with supercritical nonlinearity
- Non-degeneracy of multi-peak solutions for the Schrödinger-Poisson problem
- Gagliardo-Nirenberg-type inequalities using fractional Sobolev spaces and Besov spaces
- Ground states of Schrödinger systems with the Chern-Simons gauge fields
- Quasilinear problems with nonlinear boundary conditions in higher-dimensional thin domains with corrugated boundaries
- A system of equations involving the fractional p-Laplacian and doubly critical nonlinearities
- A modified Picone-type identity and the uniqueness of positive symmetric solutions for a prescribed mean curvature problem
- On a version of hybrid existence result for a system of nonlinear equations
- Special Issue: Geometric PDEs and applications
- Preface for the special issue on “Geometric Partial Differential Equations and Applications”
- Convex hypersurfaces with prescribed Musielak-Orlicz-Gauss image measure
- Total mean curvatures of Riemannian hypersurfaces
- On degenerate case of prescribed curvature measure problems
- A curvature flow to the Lp Minkowski-type problem of q-capacity
- Aleksandrov reflection for extrinsic geometric flows of Euclidean hypersurfaces
- A note on second derivative estimates for Monge-Ampère-type equations
- The Lp chord Minkowski problem
- Widths of balls and free boundary minimal submanifolds
- Smooth approximation of twisted Kähler-Einstein metrics
- The exterior Dirichlet problem for the homogeneous complex k-Hessian equation
- A Carleman inequality on product manifolds and applications to rigidity problems
- Asymptotic behavior of solutions to the Monge-Ampère equations with slow convergence rate at infinity
- Pinched hypersurfaces are compact
- The spinorial energy for asymptotically Euclidean Ricci flow
- Geometry of CMC surfaces of finite index
- Capillary Schwarz symmetrization in the half-space
- Regularity of optimal mapping between hypercubes
- Special Issue: In honor of David Jerison
- Preface for the special issue in honor of David Jerison
- Homogenization of oblique boundary value problems
- A proof of a trace formula by Richard Melrose
- Compactness estimates for minimizers of the Alt-Phillips functional of negative exponents
- Regularity properties of monotone measure-preserving maps
- Examples of non-Dini domains with large singular sets
- Sharp inequalities for coherent states and their optimizers
- Gradient estimates and the fundamental solution for higher-order elliptic systems with lower-order terms
- Propagation of symmetries for Ricci shrinkers
- Linear extension operators for Sobolev spaces on radially symmetric binary trees
- The Neumann problem on the domain in 𝕊3 bounded by the Clifford torus
- On an effective equation of the reduced Hartree-Fock theory
- Polynomial sequences in discrete nilpotent groups of step 2
- Integral inequalities with an extended Poisson kernel and the existence of the extremals
- On singular solutions of Lane-Emden equation on the Heisenberg group
Creative Commons
BY 4.0
Artikel in diesem Heft
- Research Articles
- Asymptotic properties of critical points for subcritical Trudinger-Moser functional
- The existence of positive solution for an elliptic problem with critical growth and logarithmic perturbation
- On some dense sets in the space of dynamical systems
- Sharp profiles for diffusive logistic equation with spatial heterogeneity
- Generic properties of the Rabinowitz unbounded continuum
- Global bifurcation of coexistence states for a prey-predator model with prey-taxis/predator-taxis
- Multiple solutions of p-fractional Schrödinger-Choquard-Kirchhoff equations with Hardy-Littlewood-Sobolev critical exponents
- Improved fractional Trudinger-Moser inequalities on bounded intervals and the existence of their extremals
- The existence of infinitely many boundary blow-up solutions to the p-k-Hessian equation
- A priori bounds, existence, and uniqueness of smooth solutions to an anisotropic Lp Minkowski problem for log-concave measure
- Existence of nonminimal solutions to an inhomogeneous elliptic equation with supercritical nonlinearity
- Non-degeneracy of multi-peak solutions for the Schrödinger-Poisson problem
- Gagliardo-Nirenberg-type inequalities using fractional Sobolev spaces and Besov spaces
- Ground states of Schrödinger systems with the Chern-Simons gauge fields
- Quasilinear problems with nonlinear boundary conditions in higher-dimensional thin domains with corrugated boundaries
- A system of equations involving the fractional p-Laplacian and doubly critical nonlinearities
- A modified Picone-type identity and the uniqueness of positive symmetric solutions for a prescribed mean curvature problem
- On a version of hybrid existence result for a system of nonlinear equations
- Special Issue: Geometric PDEs and applications
- Preface for the special issue on “Geometric Partial Differential Equations and Applications”
- Convex hypersurfaces with prescribed Musielak-Orlicz-Gauss image measure
- Total mean curvatures of Riemannian hypersurfaces
- On degenerate case of prescribed curvature measure problems
- A curvature flow to the Lp Minkowski-type problem of q-capacity
- Aleksandrov reflection for extrinsic geometric flows of Euclidean hypersurfaces
- A note on second derivative estimates for Monge-Ampère-type equations
- The Lp chord Minkowski problem
- Widths of balls and free boundary minimal submanifolds
- Smooth approximation of twisted Kähler-Einstein metrics
- The exterior Dirichlet problem for the homogeneous complex k-Hessian equation
- A Carleman inequality on product manifolds and applications to rigidity problems
- Asymptotic behavior of solutions to the Monge-Ampère equations with slow convergence rate at infinity
- Pinched hypersurfaces are compact
- The spinorial energy for asymptotically Euclidean Ricci flow
- Geometry of CMC surfaces of finite index
- Capillary Schwarz symmetrization in the half-space
- Regularity of optimal mapping between hypercubes
- Special Issue: In honor of David Jerison
- Preface for the special issue in honor of David Jerison
- Homogenization of oblique boundary value problems
- A proof of a trace formula by Richard Melrose
- Compactness estimates for minimizers of the Alt-Phillips functional of negative exponents
- Regularity properties of monotone measure-preserving maps
- Examples of non-Dini domains with large singular sets
- Sharp inequalities for coherent states and their optimizers
- Gradient estimates and the fundamental solution for higher-order elliptic systems with lower-order terms
- Propagation of symmetries for Ricci shrinkers
- Linear extension operators for Sobolev spaces on radially symmetric binary trees
- The Neumann problem on the domain in 𝕊3 bounded by the Clifford torus
- On an effective equation of the reduced Hartree-Fock theory
- Polynomial sequences in discrete nilpotent groups of step 2
- Integral inequalities with an extended Poisson kernel and the existence of the extremals
- On singular solutions of Lane-Emden equation on the Heisenberg group
