Beyond the classical strong maximum principle: sign-changing forcing term and flat solutions
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Publication:6119532
DOI10.1515/anona-2023-0128arXiv2308.02626MaRDI QIDQ6119532
Jesús Ildefonso Díaz, Jesus Hernandez
Publication date: 1 March 2024
Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2308.02626
heat equationunique continuationstrong maximum principlepositive flat solutionssign-changing forcing term
Maximum principles in context of PDEs (35B50) Second-order elliptic equations (35J15) Continuation and prolongation of solutions to PDEs (35B60) Second-order parabolic equations (35K10) Positive solutions to PDEs (35B09)
Cites Work
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- Positive and nodal solutions bifurcating from the infinity for a semilinear equation: solutions with compact support
- On the free boundary associated with the stationary Monge-Ampère operator on the set of non strictly convex functions
- Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for \(N \geq 3\)
- On the retention of the interfaces in some elliptic and parabolic nonlinear problems
- On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via flat solutions: the one-dimensional case
- On very weak solutions of semi-linear elliptic equations in the framework of weighted spaces with respect to the distance to the boundary
- Green function for Schrödinger operator and conditioned Feynman-Kac gauge
- Remarks on the strong maximum principle.
- The strong maximum principle revisited.
- Positivity for large time of solutions of the heat equation: the parabolic antimaximum principle.
- The fractional Schrödinger equation with general nonnegative potentials. The weighted space approach
- Hopf potentials for the Schrödinger operator
- Linear diffusion with singular absorption potential and/or unbounded convective flow: the weighted space approach
- On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via singular potentials: the multi-dimensional case
- Correction to: ``On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via singular potentials: the multi-dimensional case
- On the linearization of some singular, nonlinear elliptic problems and applications
- Blow up for \(u_ t- \Delta u=g(u)\) revisited
- Existence results for elliptic problems with gradient terms via a priori estimates
- Linearized stability for degenerate and singular semilinear and quasilinear parabolic problems: the linearized singular equation
- A strong maximum principle for some quasilinear elliptic equations
- Hopf boundary maximum principle violation for semilinear elliptic equations
- On the exact multiplicity of stable ground states of non-Lipschitz semilinear elliptic equations for some classes of starshaped sets
- On the existence of positive solutions and solutions with compact support for a spectral nonlinear elliptic problem with strong absorption
- Remarks on sublinear elliptic equations
- The Asymptotic Behavior of the Solutions of Degenerate Parabolic Equations
- An elliptic equation with singular nonlinearity
- SOLUTIONS WITH COMPACT SUPPORT OF VARIATIONAL INEQUALITIES
- Existence and uniqueness of solutions of Schrödinger type stationary equations with very singular potentials without prescribing boundary conditions and some applications
- Global bifurcation and continua of nonnegative solutions for a quasilinear elliptic problem
- A Liouville-type theorem in a half-space and its applications to the gradient blow-up behavior for superquadratic diffusive Hamilton–Jacobi equations
- The normal derivative lemma and surrounding issues
- Boundary Harnack Estimates and Quantitative Strong Maximum Principles for Uniformly Elliptic PDE
- A Remark on Linear Elliptic Differential Equations of Second Order
- New applications of monotonicity methods to a class of non-monotone parabolic quasilinear sub-homogeneous problems
- The uniform Hopf inequality for discontinuous coefficients and optimal regularity in BMO for singular problems