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Minimal support results for Schrödinger equations
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Laura De Carli
Veröffentlicht/Copyright:
28. September 2012
Abstract
We consider a number of linear and non-linear boundary value problems involving generalized Schrödinger equations. The model case is -Δu = Vu for u ∈ W01,2(D) with D a bounded domain in ℝn. We use the Sobolev embedding theorem, and in some cases the Moser–Trudinger inequality and the Hardy–Sobolev inequality, to derive necessary conditions for the existence of nontrivial solutions.
These conditions usually involve a lower bound for a product of powers of the norm of V, the measure of D, and a sharp Sobolev constant. In most cases, these inequalities are best possible.
Received: 2012-7-25
Published Online: 2012-9-28
Published in Print: 2015-1-1
© 2015 by De Gruyter
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Artikel in diesem Heft
- Frontmatter
- On the character degrees of Sylow p-subgroups of Chevalley groups G(pf) of type E
- Achievable sets in ℤn
- A criterion on oscillation and variation for the commutators of singular integral operators
- Some 𝐇1𝔉-groups with unbounded torsion and a conjecture of Kropholler and Mislin
- Goodwillie calculus and Whitehead products
- Computing Borel's regulator
- Applications of a transcendence criterion for reciprocal sums of binary linear recurrences
- BSDE and generalized Dirichlet forms: The infinite dimensional case
- Faithful representations of infinite-dimensional nilpotent Lie algebras
- Locally finitely presented categories with no flat objects
- A common generalization of metric, ultrametric and topological fixed point theorems
- Correction to A common generalization of metric, ultrametric and topological fixed point theorems [Forum Math. 27 (2015), 303–327]
- Erdős–Rényi graph, Szemerédi–Trotter type theorem, and sum-product estimates over finite rings
- Minimal support results for Schrödinger equations
- Dynamics for the focusing, energy-critical nonlinear Hartree equation
- A fixed point theorem for Lie groups acting on buildings and applications to Kac–Moody theory
- On effective determination of Maass forms from central values of Rankin–Selberg L-function
- On embedding left-ordered groups into division rings
- Conservation property of symmetric jump-diffusion processes
- Irreducible representations of Leavitt path algebras
- Commutators of elements of coprime orders in finite groups
- Endoscopy and the transfer from GSp(4) to GL(4)
- Cycles in Leavitt path algebras by means of idempotents
- On volumes determined by subsets of Euclidean space
Schlagwörter für diesen Artikel
Schrödinger equation;
Sobolev embedding theorem;
Moser–Trudinger inequality
Artikel in diesem Heft
- Frontmatter
- On the character degrees of Sylow p-subgroups of Chevalley groups G(pf) of type E
- Achievable sets in ℤn
- A criterion on oscillation and variation for the commutators of singular integral operators
- Some 𝐇1𝔉-groups with unbounded torsion and a conjecture of Kropholler and Mislin
- Goodwillie calculus and Whitehead products
- Computing Borel's regulator
- Applications of a transcendence criterion for reciprocal sums of binary linear recurrences
- BSDE and generalized Dirichlet forms: The infinite dimensional case
- Faithful representations of infinite-dimensional nilpotent Lie algebras
- Locally finitely presented categories with no flat objects
- A common generalization of metric, ultrametric and topological fixed point theorems
- Correction to A common generalization of metric, ultrametric and topological fixed point theorems [Forum Math. 27 (2015), 303–327]
- Erdős–Rényi graph, Szemerédi–Trotter type theorem, and sum-product estimates over finite rings
- Minimal support results for Schrödinger equations
- Dynamics for the focusing, energy-critical nonlinear Hartree equation
- A fixed point theorem for Lie groups acting on buildings and applications to Kac–Moody theory
- On effective determination of Maass forms from central values of Rankin–Selberg L-function
- On embedding left-ordered groups into division rings
- Conservation property of symmetric jump-diffusion processes
- Irreducible representations of Leavitt path algebras
- Commutators of elements of coprime orders in finite groups
- Endoscopy and the transfer from GSp(4) to GL(4)
- Cycles in Leavitt path algebras by means of idempotents
- On volumes determined by subsets of Euclidean space
