A fully anisotropic Sobolev inequality

By Andrea Cianchi. 2000

90 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/090c8f2fb55f5e34396c6cc97d816d98ed42db25

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Iwona Chlebicka
2. Andrea Cianchi
3. Paolo Marcellini
4. Giuseppe Mingione
5. Cristina Tarsi
6. Robert J. Berman
7. G. Lu
8. Nguyen Huong Lam

In Computational Theory and Mathematics

1. Iwona Chlebicka
2. Andrea Cianchi
3. Paolo Marcellini
4. Giuseppe Mingione
5. Robert J. Berman
6. G. Lu
7. Nguyen Huong Lam
8. Giulio Ciraolo

In Mathematical Physics

1. Iwona Chlebicka
2. Andrea Cianchi
3. Paolo Marcellini
4. Giuseppe Mingione
5. Giulio Ciraolo

Citations in the corpus

• Fully anisotropic elliptic problems with minimally integrable data (2019, unknown): “s requires some further definitions. Assume that (2.49) Z 0 t Φ◦(t) 1 n−1 dt<∞. If (2.50) Z∞ t Φ◦(t) 1 n−1 dt= ∞, then we denote by Φn : [0,∞) → [0,∞] the Sobolev conjugate of Φ introduced in [Ci2]. Namely, Φn is the Young function defined as (2.51) Φn(t) = Φ◦(H−1(t)) for t≥ 0, FULLY ANISOTROPIC ”
• Optimal Orlicz-Sobolev embeddings (2004, result): “4, involving A instead of A, may be proved; hence, one can recover the optimal embedding, established in [14], for W 1,A 0 (G) into the Orlicz space associated with the Young function (A )n defined as in (1.”
• Symmetrization and second-order Sobolev inequalities (2004, background): “Inequality (5.8) is proved in Lemma 1 of [10] with A p replaced by an equivalent Young function (for such equivalence, see e.g. Lemma 2 of [ 12 ]).”
• Symmetrization in Anisotropic Elliptic Problems (2007, methodology): “In this connection, key tools are some recent inequalities in Orlicz and Orlicz-Sobolev spaces appearing in Cianchi (1996, 2000a, 2004), which also enable us to provide an appropriate functional framework for the problems under consideration.”
• A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, methodology): “It has been developed in PDE context in [52, 55] and applied in studies on existence and regularity [9, 15, 14, 10, 11, 18].”
• Nonlinear parabolic problems in Musielak--Orlicz spaces (2013, unknown): “[9].”