A ground state alternative for singular Schrodinger operators

By Yehuda Pinchover, Kyril Tintarev. 2004

70 citations recorded by the source corpus.

Let a be a quadratic form associated with a Schrodinger operator L =− ∇ ·(A∇) + V on a domain ⊂ R d .I fa is nonnegative on C ∞ 0 (), then either there is W> 0 such that

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/72bdaa54a4352ddaa5f8e6b3c6e270ad2b5e2183

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In Applied Mathematics

1. Vitaly Moroz
2. Jean Van Schaftingen
3. C. Tintarev
4. Hongyu Ye
5. Minbo Yang
6. Daniele Cassani
7. Jianjun Zhang
8. Claudianor Oliveira Alves

In Computational Theory and Mathematics

1. Vitaly Moroz
2. Jean Van Schaftingen
3. C. Tintarev
4. Franz Gmeineder
5. Bogdan Raiță
6. Jiankang Xia

In Mathematical Physics

1. Vitaly Moroz
2. Jean Van Schaftingen
3. C. Tintarev
4. Hongyu Ye
5. Minbo Yang
6. Jiankang Xia
7. Binlin Zhang
8. Xianhua Tang

Citations in the corpus

• Semi-classical states for the Choquard equation (2013, background): “…For a nonempty open set Ω ⊆ R N , we denote by H 1 V, 0 (Ω) the Hilbert space obtained by completion of the set of smooth test functions C ∞ c (Ω) with respect to the norm ) cannot be identified as a space of measurable functions or a space of distributions (see [46, Section 1] for a discussion).”
• Trudinger-Moser inequality with remainder terms (2012, background): “Ground state alternative We summarize first some relevant results on positive elliptic operators with singular potentials, drawing upon [18].”
• OPTIMAL HARDY WEIGHT FOR SECOND-ORDER ELLIPTIC OPERATOR: AN ANSWER TO A PROBLEM OF AGMON (2012, unknown): “Since P is subcritical, we know that D(1,2) P (Ω) →֒W 1,2 loc (Ω) (see [50]) and λ0(P,W,Ω) is characterized by the Rayleigh-Ritz variational problem: λ0 = inf u∈D(1,2) P (Ω)\{0} q(u)”