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Liouville theorems in halfspaces for parabolic hypoelliptic equations

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Abstract

We prove some one-side Liouville-type theorems in halfspaces for a class of evolution hypoelliptic equations. The operators we deal with are left translation invariant, and homogeneous of degree two, on homogeneous Lie groups on \(\mathbb{R}^{N + 1}\).

Keywords: Parabolic operators, Liouville Theorems, Liouville Theorems in halfspaces

Mathematics Subject Classification (2000): 35K65, 35H10, 35B99

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References

  • 1. Bear, H.S.: Liouville theorems for heat functions. Comm. Partial Differential Equations 11, 1605–1625 (1986)

    Google Scholar 

  • 2. Bony, J.M.: Principe de maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés. Ann. Inst. Fourier, Grenoble 19, 277–304 (1969)

    Google Scholar 

  • 3. Glagoleva, R.Ya.: Liouville theorems for the solution of a second order linear parabolic equation with discontinuous coefficients. Mat. Zametki 5, 599–606 (1969)

    Google Scholar 

  • 4. Glagoleva, R.Ya.: Phragmen-Liouville-type theorems and Liouville theorems for a linear parabolic equation. Mat. Zametki 37, 119–124 (1985)

    Google Scholar 

  • 5. Gutierrez, C.E., Lanconelli, E.: Classical, viscosity and average solutions for PDE's with nonnegative characteristic form. Rend. Mat. Acc. Lincei, Serie IX 15, 17–28 (2004)

    Google Scholar 

  • 6. Hirschman, Jr., I.I.: A note on the heat equation. Duke J. 19, 487–492 (1952)

    Google Scholar 

  • 7. Kogoj A.E., Lanconelli E.: An invariant Harnack inequality for a class of hypoelliptic ultraparabolic equations. Mediterr. J. Math. 1, 51–80 (2004)

    Google Scholar 

  • 8. Kogoj A.E., Lanconelli, E.: One-Side Liouville Theorems for a Class of Hypoelliptic Ultraparabolic Equations. Contemporary Math. 368, 305–312 (2005)

    Google Scholar 

  • 9. Tavkhelidze, I.N.: Liouville's Theorems for second-order elliptic and parabolic equations. Vestnik Moskovskogo Universiteta. Matematika 31, 28–35 (1976)

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Piazza di Porta San Donato, 5, I–40126 Bologna, Italy

    Alessia E. Kogoj

  2. Dipartimento di Matematica, Piazza di Porta San Donato, 5, I–40126 Bologna, Italy

    Ermanno Lanconelli

Authors
  1. Alessia E. Kogoj
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  2. Ermanno Lanconelli
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Kogoj, A.E., Lanconelli, E. Liouville theorems in halfspaces for parabolic hypoelliptic equations. Ricerche mat. 55, 107–122 (2006). https://doi.org/10.1007/s11587-006-0015-9

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  • DOI: https://doi.org/10.1007/s11587-006-0015-9

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