Welcome to the Personal webpage of Bruno Premoselli 

Publications:

• A priori bounds for energy-bounded solutions of critical polyharmonic equations (with L. Carletti), 59 pages, 2026. arXiv:2605.29690

• Compactness of conformal metrics with constant $Q$-curvature of higher order (with S. Mazumdar), 50 pages, 2025. Accepted for publication in Proceedings of the London Mathematical Society. arXiv:2510.00888

• Least-energy solutions of the Brézis-Nirenberg problem in dimension 3 (with H. Cheikh-Ali), 60 pages, 2025. Accepted for publication in the Journal of the EMS. arXiv:2509.19145. 

• Extremising eigenvalues of the GJMS operator in a fixed conformal class (with E. Humbert and R.Pétrides), 96 pages, 2025. arXiv: 2505.08280.

• Compactness results for Sign-Changing Solutions of critical nonlinear elliptic equations of low energy  (with H. Cheikh-Ali), Analysis and PDEs Vol. 19, no.3, 2026. arXiv:2412.00817

• Non-existence of minimizers for the second conformal eigenvalue near the round sphere in low dimensions (with J. Vétois), 35 pages, 2024. Accepted for publication in the Journal of Differential Geometry. arXiv:2408.07823

• One-bubble nodal blow-up for asymptotically critical stationary Schrödinger-type equation (with F. Robert), Journal of Functional Analyis Volume 288, Issue 6, 15 March 2025 arXiv:2404.16384. 

• Classification of radial blow-up at the first critical exponent for the Lin-Ni-Takagi problem in the ball (with D. Bonheure and J.-B. Casteras), Mathematische Annalen Volume 390, Issue 4, December 2024. arXiv:2211.08962.

• Sign-changing blow-up for the Yamabe equation at the lowest energy level (with J. Vetois), Advances in Mathematics 410 Part B, 2022. arXiv:2206.08770

• Stability and Instability results for sign-changing solutions to second-order critical elliptic equations (with J. Vetois), Journal de Mathématiques Pures et Appliquées, no. 167 (November 2022), 257-293. arXiv:2201.05679

• A priori estimates for finite-energy sign-changing blowing-up solutions of critical elliptic equations, International Mathematical Research Notices, Vol 2024, Issue 6, March 2024, 5212–5273. arXiv:2111.02470

• Towers of bubbles for Yamabe-type equations and for the Brézis-Nirenberg problem in dimensions $n \ge 7$. Journal of Geometric Analysis no. 32, Article number 73 (2022). arXiv:2009.01515

• Singular perturbations of critical nonlinear elliptic equations in dimension $3$, 21 pages, 2020. Discrete and Continuous Dynamical Systems, no. 41 (2021), issue 11, 5087-5103.  

• Compactness of sign-changing solutions to scalar curvature-type equations with bounded negative part (with J. Vétois),  J. Differential Equations 266 (2019), no. 11, 7416–7458. 

• Examples of compact Einstein four-manifolds with negative curvature (with J. Fine), J. Amer. Math. Soc. 33 (2020), 991-1038. arXiv:1802.00608

• Bubbling above the threshold of the scalar curvature in dimensions four and five (with P-D. Thizy), Calculus of Variations and PDEs no. 57, Article number: 147 (2018), 39 pages.  hal-01805092

• A pointwise finite-dimensional reduction method for Einstein-Lichnerowicz type systems: the six-dimensional case, Nonlinear Analysis no. 172 (2018), 200--215.

• A pointwise finite-dimensional reduction method for a fully coupled system of Einstein-Lichnerowicz type, Communications in Contemporary Mathematics 20 (2018), no. 6, 1750076, 72 pp. arXiv:1605.05468

• Non-compactness and infinite number of conformal initial data sets in high dimensions (with J. Wei), Journal of Functional Analysis 270 (2016), no.2, 718--747. arXiv:1505.02806 

• Stability and instability of the $n$-dimensional Einstein-Lichnerowicz constraints system,  International Mathematical Research Notices Vol. 2016 no.8, 1951-2025. arXiv:1502.04233

• Stability of the Einstein-Lichnerowicz constraints system (with O. Druet), Mathematische Annalen 362 (2015), no.3, 839-886. arXiv:1312.6574

• Effective multiplicity for the Einstein-scalar field Lichnerowicz equation, Calculus of variations and Partial Differential Equations 53 (2015), no.1, 29-64. arXiv:1307.2416

• The Einstein-scalar field constraint system in the positive case, Communications in Mathematical Physics 326 (2014), no. 2, 543-557. arXiv:1301.5792
  
  

Conference Proceedings:

• Negatively curved Einstein metrics on ramified covers of closed four-dimensional hyperbolic manifolds. To appear in Actes du Séminaire de Théorie Spectrale et Géométrie de l'Insitut Fourier

• A pointwise finite-dimensional reduction method for Einstein-Lichnerowciz type systems, Proceedings of the BruTo PDE's Conference (Torino, 2--5 May 2016). Rend. Semin. Mat. Univ. Politec. Torino 74 (2016), no. 2, 81–93.