{"id":{"repo_id":"missouri","oai_identifier":"oai:mospace.umsystem.edu:10355/86507"},"canonical_url":"https://search.dev.ndltd.org/etd/missouri/oai:mospace.umsystem.edu:10355/86507","repository":{"repo_id":"missouri","name":"University of Missouri","base_url":"https://mospace.umsystem.edu/oai/request"},"display":{"title":"Adams inequalities with exact growth condition : on Rn and the Heisenberg group","abstract":"In this thesis we prove sharp Adams inequality with exact growth condition for the Riesz potential as well as the more general strictly Riesz-like potentials on R[superscript n]. Then we derive the Moser-Trudinger type inequality with exact growth condition for fractional Laplacians with arbitrary 0 [less than] [alpha] [less than] n, higher order gradients and homogeneous elliptic differential operators. Next we give an application to a quasilinear elliptic equation, and prove the existence of ground state solution of this equation. Lastly, we extend our result to the Heisenberg group. By applying the same technique used in R[superscript n], we derive a sharp Adams inequality with critical growth condition on H[superscript n] for integral operators whose kernels are strictly Riesz-like on H[superscript n]. As a consequence we then derive the corresponding sharp Moser-Trudinger inequalities with exact growth condition for the powers of sublaplacian -L[subscript 0] [superscript alpha/2] when [alpha] is an even integer, and for the subgradient [del] H[subscript n].","abstract_html":"In this thesis we prove sharp Adams inequality with exact growth condition for the Riesz potential as well as the more general strictly Riesz-like potentials on R[superscript n]. Then we derive the Moser-Trudinger type inequality with exact growth condition for fractional Laplacians with arbitrary 0 [less than] [alpha] [less than] n, higher order gradients and homogeneous elliptic differential operators. Next we give an application to a quasilinear elliptic equation, and prove the existence of ground state solution of this equation. Lastly, we extend our result to the Heisenberg group. By applying the same technique used in R[superscript n], we derive a sharp Adams inequality with critical growth condition on H[superscript n] for integral operators whose kernels are strictly Riesz-like on H[superscript n]. As a consequence we then derive the corresponding sharp Moser-Trudinger inequalities with exact growth condition for the powers of sublaplacian -L[subscript 0] [superscript alpha/2] when [alpha] is an even integer, and for the subgradient [del] H[subscript n].","abstract_has_math":false,"creators":["Qin, Liuyu"],"institution":"University of Missouri--Columbia","degree_name":"Ph. 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Then we derive the Moser-Trudinger type inequality with exact growth condition for fractional Laplacians with arbitrary 0 [less than] [alpha] [less than] n, higher order gradients and homogeneous elliptic differential operators. Next we give an application to a quasilinear elliptic equation, and prove the existence of ground state solution of this equation. Lastly, we extend our result to the Heisenberg group. By applying the same technique used in R[superscript n], we derive a sharp Adams inequality with critical growth condition on H[superscript n] for integral operators whose kernels are strictly Riesz-like on H[superscript n]. As a consequence we then derive the corresponding sharp Moser-Trudinger inequalities with exact growth condition for the powers of sublaplacian -L[subscript 0] [superscript alpha/2] when [alpha] is an even integer, and for the subgradient [del] H[subscript n]."]},{"key":"dc:title","label":"Title","values":["Adams inequalities with exact growth condition : on Rn and the Heisenberg group"]}]}],"canonical_facts":{"dc:contributor.advisor":["Morpurgo, Carlo"],"dc:creator":["Qin, Liuyu"],"dc:date.accessioned":["2021-08-10T15:55:51Z"],"dc:date.available":["2021-08-10T15:55:51Z"],"dc:date.issued":["2020"],"dc:description.abstract":["In this thesis we prove sharp Adams inequality with exact growth condition for the Riesz potential as well as the more general strictly Riesz-like potentials on R[superscript n]. Then we derive the Moser-Trudinger type inequality with exact growth condition for fractional Laplacians with arbitrary 0 [less than] [alpha] [less than] n, higher order gradients and homogeneous elliptic differential operators. Next we give an application to a quasilinear elliptic equation, and prove the existence of ground state solution of this equation. Lastly, we extend our result to the Heisenberg group. By applying the same technique used in R[superscript n], we derive a sharp Adams inequality with critical growth condition on H[superscript n] for integral operators whose kernels are strictly Riesz-like on H[superscript n]. As a consequence we then derive the corresponding sharp Moser-Trudinger inequalities with exact growth condition for the powers of sublaplacian -L[subscript 0] [superscript alpha/2] when [alpha] is an even integer, and for the subgradient [del] H[subscript n]."],"dc:identifier.doi":["https://doi.org/10.32469/10355/86507"],"dc:identifier.uri":["https://hdl.handle.net/10355/86507"],"dc:language":["English"],"dc:language.iso":["eng"],"dc:publisher":["University of Missouri--Columbia"],"dc:rights":["OpenAccess."],"dc:title":["Adams inequalities with exact growth condition : on Rn and the Heisenberg group"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics (MU)"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["University of Missouri--Columbia"]},"updated_at":"2026-07-24T03:09:39Z"}