Rigidity of solutions to elliptic equations with one uniform limit

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Entire solutions to PDEs (35B08) Symmetries, invariants, etc. in context of PDEs (35B06) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

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Qualitative properties and classification of nonnegative solutions to $-\Delta u=f(u)$ in unbounded domains when $f(0) < 0$
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Inequalities for second-order elliptic equations with applications to unbounded domains. I
Some results about semilinear elliptic problems on half-spaces
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An application of a global lifting method for homogeneous Hörmander vector fields to the Gibbons conjecture
The sliding methods for the fractional $p$-Laplacian
Regularity of flat level sets in phase transitions
Schrödinger operators with singular potentials
The Liouville property and a conjecture of De Giorgi.
Rigidity results for elliptic PDEs with uniform limits: an abstract framework with applications
$1$D symmetry for solutions of semilinear and quasilinear elliptic equations
Monotonicity and rigidity of solutions to some elliptic systems with uniform limits
Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi

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