Uneingeschränkter Zugang

Symmetrization for Mixed Operators

   | 27. Apr. 2024

Zitieren

A. Alvino, G. Trombetti, and P.-L. Lions, On optimization problems with prescribed rearrangements, Nonlinear Anal. 13 (1989), no. 2, 185–220. Search in Google Scholar

S. Biagi, S. Dipierro, E. Valdinoci, and E. Vecchi, Semilinear elliptic equations involving mixed local and nonlocal operators, Proc. Roy. Soc. Edinburgh Sect. A 151 (2021), no. 5, 1611–1641. Search in Google Scholar

S. Biagi, S. Dipierro, E. Valdinoci, and E. Vecchi, A Hong–Krahn–Szegö inequality for mixed local and nonlocal operators, Math. Eng. 5 (2022), no. 1, Paper No. 014, 25 pp. Search in Google Scholar

S. Biagi, S. Dipierro, E. Valdinoci, and E. Vecchi, Mixed local and nonlocal elliptic operators: regularity and maximum principles, Comm. Partial Di˙erential Equations 47 (2022), no. 3, 585–629. DOI: 10.1080/03605302.2021.1998908. Search in Google Scholar

S. Biagi, S. Dipierro, E. Valdinoci, and E. Vecchi, A Faber–Krahn inequality for mixed local and nonlocal operators, J. Anal. Math. 150 (2023), no. 2, 405–448. Search in Google Scholar

L. Brasco, E. Lindgren, and E. Parini, The fractional Cheeger problem, Interfaces Free Bound. 16 (2014), no. 3, 419–458. Search in Google Scholar

C. Bucur, Some observations on the Green function for the ball in the fractional Laplace framework, Commun. Pure Appl. Anal. 15 (2016), no. 2, 657–699. Search in Google Scholar

D. Chen and H. Li, Talenti’s comparison theorem for Poisson equation and applications on Riemannian manifold with nonnegative Ricci curvature, J. Geom. Anal. 33 (2023), Paper No. 123, 20 pp. DOI: 10.1007/s12220-022-01162-0. Search in Google Scholar

Z.-Q. Chen, P. Kim, R. Song, and Z. Vondraček, Sharp Green function estimates for Δ+Δα2 \Delta + {\Delta ^{{\alpha \over 2}}} in C1,1 open sets and their applications, Illinois J. Math. 54 (2010), no. 3, 981–1024. Search in Google Scholar

Z.-Q. Chen and T. Kumagai, A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for di˙usions with jumps, Rev. Mat. Iberoam. 26 (2010), no. 2, 551–589. Search in Google Scholar

V. Ferone and B. Volzone, Symmetrization for fractional elliptic problems: a direct approach, Arch. Ration. Mech. Anal. 239 (2021), no. 3, 1733–1770. Search in Google Scholar

V. Ferone and B. Volzone, Symmetrization for fractional nonlinear elliptic problems, Discrete Contin. Dyn. Syst. 43 (2023), no. 3–4, 1400–1419. Search in Google Scholar

H. Hajaiej and K. Perera, Ground state and least positive energy solutions of elliptic problems involving mixed fractional p-Laplacians, Di˙erential Integral Equations 35 (2022), no. 3–4, 173–190. Search in Google Scholar

S. Kesavan, Some remarks on a result of Talenti, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988), no. 3, 453–465. Search in Google Scholar

T. Kulczycki, Properties of Green function of symmetric stable processes, Probab. Math. Statist. 17, Acta Univ. Wratislav. No. 2029 (1997), no. 2, 339–364. Search in Google Scholar

E.H. Lieb and M. Loss, Analysis, Graduate Studies in Mathematics, 14, American Mathematical Society, Providence, RI, 2001. Search in Google Scholar

P.-L. Lions, Quelques remarques sur la symétrisation de Schwartz, in: H. Brézis, J.-L. Lions (eds.), Nonlinear Partial Di˙erential Equations and Their Applications. Collège de France Seminar. Vol. I, Res. Notes in Math., 53, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1981, pp. 308–319. Search in Google Scholar

P. Mironescu and W. Sickel, A Sobolev non embedding, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 26 (2015), no. 3, 291–298. Search in Google Scholar

G. Talenti, Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), no. 4, 697–718. Search in Google Scholar

eISSN:
2391-4238
Sprache:
Englisch
Zeitrahmen der Veröffentlichung:
2 Hefte pro Jahr
Fachgebiete der Zeitschrift:
Mathematik, Allgemeines