Recent progress on stable and finite Morse index solutions of semilinear elliptic equations (Q2055198)

scientific article; zbMATH DE number 7438956

Language	Label	Description	Also known as
English	Recent progress on stable and finite Morse index solutions of semilinear elliptic equations	scientific article; zbMATH DE number 7438956

Statements

instance of

scholarly article

0 references

title

Recent progress on stable and finite Morse index solutions of semilinear elliptic equations (English)

0 references

author

Kelei Wang

0 references

published in

Electronic Research Archive

0 references

publication date

3 December 2021

0 references

zbMATH Keywords

semilinear equation with Laplacian

0 references

stable solutions

0 references

finite Morse index solutions

0 references

Liouville theorem

0 references

De Giorgi conjecture

0 references

MaRDI profile type

Publication

0 references

full work available at URL

https://doi.org/10.3934/era.2021062

0 references

cites work

Higher-Dimensional Catenoid, Liouville Equation, and Allen–Cahn Equation

0 references

Q3895957

0 references

Q3732212

0 references

Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi

0 references

Q4466537

0 references

Stable $s$-minimal cones in $\mathbb{R}^3$ are flat for $s \sim 1$

0 references

Stable solutions to semilinear elliptic equations are smooth up to dimension $9$

0 references

Nonlocal minimal surfaces

0 references

Regularity properties of nonlocal minimal surfaces via limiting arguments

0 references

Global energy minimizers for free boundary problems and full regularity in three dimensions

0 references

The structure of stable minimal hypersurfaces in $\mathbb{R}^{n+1}$

0 references

Minimal surfaces and the Allen-Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates

0 references

Stable and finite Morse Index solutions on R^n or on bounded domains with small diffusion II

0 references

Stable solutions on $\mathbb R^n$ and the primary branch of some non-self-adjoint convex problems.

0 references

Stable and finite Morse index solutions on 𝐑ⁿ or on bounded domains with small diffusion

0 references

Supercritical finite Morse index solutions

0 references

Finite Morse index solutions of exponential problems

0 references

Finite Morse index solutions of supercritical problems

0 references

Q3645988

0 references

Q3096677

0 references

New Results for Finite Morse Index Solutions on ℝ<sup>N</sup> and applications

0 references

Finite Morse index solutions of an elliptic equation with supercritical exponent

0 references

On the classification of solutions of -Δ𝑢=𝑒^{𝑢} on ℝ^{ℕ}: Stability outside a compact set and applications

0 references

Non-radial singular solutions of Lane-Emden equations in $\mathbb{R}^N$

0 references

Partial regularity of finite Morse index solutions to the Lane-Emden equation

0 references

A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem

0 references

On the fractional Lane-Emden equation

0 references

Q4191164

0 references

A singular energy minimizing free boundary

0 references

Multiple-end solutions to the Allen-Cahn equation in $\mathbb R^2$

0 references

The Toda system and clustering interfaces in the Allen-Cahn equation

0 references

On De Giorgi's conjecture in dimension $N\geq 9$

0 references

Entire solutions of the Allen-Cahn equation and complete embedded minimal surfaces of finite total curvature in $\mathbb{R}^3$

0 references

Interface foliation near minimal submanifolds in Riemannian manifolds with positive Ricci curvature

0 references

The work of Norman Dancer

0 references

Positive solutions of an elliptic equation with negative exponent: stability and critical power

0 references

Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equations

0 references

Finite Morse index solutions of weighted elliptic equations and the critical exponents

0 references

Monotonicity formula and $\varepsilon$-regularity of stable solutions to supercritical problems and applications to finite Morse index solutions

0 references

Q3005146

0 references

Q3558347

0 references

On the classification of solutions of the Lane-Emden equation on unbounded domains of $\mathbb R^N$

0 references

Stable solutions of $-\delta u=e^u$ on $\mathbb R^N$

0 references

On stable and finite Morse index solutions of the nonlocal Hénon-Gelfand-Liouville equation

0 references

On stable solutions of the fractional Hénon–Lane–Emden equation

0 references

On finite Morse index solutions of higher order fractional Lane-Emden equations

0 references

On stable and finite Morse index solutions of the fractional Toda system

0 references

The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension

0 references

On global solutions to semilinear elliptic equations related to the one-phase free boundary problem

0 references

On stable solutions for boundary reactions: a De Giorgi-type result in dimension $4 + 1$

0 references

On the oriented Plateau problem

0 references

Q4462175

0 references

On a conjecture of De Giorgi and some related problems

0 references

Some energy estimates for stable solutions to fractional Allen-Cahn equations

0 references

Axially symmetric solutions of the Allen-Cahn equation with finite Morse index

0 references

On the symmetry of positive solutions of the Lane-Emden equation with supercritical exponent

0 references

Liouville type results and regularity of the extremal solutions of biharmonic equation with negative exponents

0 references

Liouville-type theorems for the fourth order nonlinear elliptic equation

0 references

A monotonicity formula and Liouville-type theorems for stable solutions of the weighted elliptic system

0 references

Stability for entire radial solutions to the biharmonic equation with negative exponents

0 references

Higher critical points in an elliptic free boundary problem

0 references

Some remarks on stability of cones for the one-phase free boundary problem

0 references

Quasilinear Dirichlet problems driven by positive sources

0 references

The regularity and stability of solutions to semilinear fourth-order elliptic problems with negative exponents

0 references

Remarks on Entire Solutions for Two Fourth-Order Elliptic Problems

0 references

Minimal hypersurfaces with finite index

0 references

Decomposition of polyharmonic operator and classification of homogeneous stable solutions

0 references

Properties of positive solutions to an elliptic equation with negative exponent

0 references

Stable and singular solutions of the equation $Delta u = 1/u$

0 references

Liouville theorems for stable at infinity solutions of Lane–Emden system

0 references

Partial regularity for weak solutions of a nonlinear elliptic equation

0 references

Convergence and partial regularity for weak solutions of some nonlinear elliptic equation: The supercritical case

0 references

Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones

0 references

Q3336116

0 references

Regularity of flat level sets in phase transitions

0 references

Q3314528

0 references

Regularity of stable minimal hypersurfaces

0 references

Curvature estimates for minimal hypersurfaces

0 references

Minimal varieties in Riemannian manifolds

0 references

Topics of stable solutions to elliptic equations

0 references

Some Liouville theorems for Hénon type elliptic equations

0 references

Partial regularity of stable solutions to the Emden equation

0 references

Partial regularity of stable solutions to the supercritical equations and its applications

0 references

Erratum to: ``Partial regularity of stable solutions to the Emden equation''

0 references

Stable and finite Morse index solutions of Toda system

0 references

Finite Morse Index Implies Finite Ends

0 references

Second order estimate on transition layers

0 references

Partial regularity for a minimum problem with free boundary

0 references

A general regularity theory for stable codimension 1 integral varifolds

0 references

Stable and finite Morse index solutions of a nonlinear elliptic system

0 references

Identifiers

zbMATH Open document ID

1480.35126

0 references

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

0 references

0 references

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:2055198