Logarithmic Sobolev and interpolation inequalities on the sphere: constructive stability results. (English) Zbl 07896320
Ann. Inst. Henri Poincaré, Anal. Non Linéaire 41, No. 5, 1289-1321 (2024); corrigendum ibid. 41, No. 5, 1323-1324 (2024).
Summary: We consider Gagliardo-Nirenberg inequalities on the sphere which interpolate between the Poincaré inequality and the Sobolev inequality, and include the logarithmic Sobolev inequality as a special case. We establish explicit stability results in the subcritical regime using spectral decomposition techniques, and entropy and carré du champ methods applied to nonlinear diffusion flows.
A correction to this paper is available.
A correction to this paper is available.
MSC:
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 58J99 | Partial differential equations on manifolds; differential operators |
| 39B62 | Functional inequalities, including subadditivity, convexity, etc. |
| 43A90 | Harmonic analysis and spherical functions |
| 49J40 | Variational inequalities |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
Keywords:
logarithmic Sobolev inequality; Gagliardo-Nirenberg inequalities; stability; sphere; spectral decompositionReferences:
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