Heat kernel estimates for operators with boundary conditions

Mathematische Nachrichten

Volumn 217, Issue , 2000, Pages 13-41

  Daners, Daniel ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

Author keywords

Heat kernel estimates; Parabolic boundary value problems

Indexed keywords

EID: 0013463865     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/1522-2616(200009)217:1<13::aid-mana13>3.0.co;2-6     Document Type: Article

References (32)

1. ADAMS, R. A.: Sobolev Spaces, Academic Press, New York, 1975
2. AMANN, H.: Linear and Quasilinear Parabolic Problems, Vol. I. Abstract Linear Theory, Birkhäuser, Basel, 1995
3. p, Differential and Integral Equations 7 (1994), 1153-1168
4. ARENDT, W.: Semigroup Properties by Gaussian Estimates. In: Nonlinear Evolution Equations and Their Applications (Kyoto 1996), 162-180, RIMS Kyoto, 1997
5. ARENDT, W., and BUKHVALOV, A. V.: Integral Representations of Resolvents and Semigroups, Forum Math. 6 (1994), 111-135
6. ARENDT, W., and ELST, A. F. M. TER: Gaussian Estimates for Second Order Elliptic Operators with Boundary Conditions, J. Operator Theory 38 (1997), 87-130
7. ARONSON, D. G.: Bounds for the Fundamental Solution of a Parabolic Equation, Bull. Amer. Math. Soc. 73 (1967), 890-896
8. ARONSON, D. G.: Non-Negative Solutions of Linear Parabolic Equations, Ann. Scuola Norm. Sup. Pisa 22 (1968), 607-694
9. ARONSON, D. G., and SERRIN, J.: Local Behavior of Solutions of Quasilinear Parabolic Equations, Arch. Rational Mech. Anal. 25 (1967), 81-122
10. AUSCHER, P.: Regularity Theorems and Heat Kernel for Elliptic Operators, J. London Math. Soc. 54 (1996), 284-296
11. AUSCHER, P., MCINTOSH, A., and TCHAMITCHIAN, P.: Heat Kernels of Second Order Complex Elliptic Operators and Applications, J. Funct. Anal. 152 (1998), 22-73
12. CARLEN, E. A., KUSUOKA, S., and STROOCK, D. W.: Upper Bounds for Symmetric Markov Transition Functions, Ann. Inst. H. Poincaré. Probab. Statist. 23 (1987), 245-287
13. DANERS, D.: Robin Boundary Value Problems on Arbitrary Domains, Trans. Amer. Math. Soc. 352 (2000), 4207-4236
14. DANERS, D.: Domain Perturbation for Linear and Nonlinear Parabolic Equations, J. Differential Equations 129 (1996), 358-402
15. DAUTRAY, R., and LIONS, J. L.: Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 5, Springer-Verlag, Berlin, 1992
16. DAVIES, E. B.: Explicit Constants for Gaussian Upper Bounds on Heat Kernels, Amer. J. Math. 109 (1987), 319-334
17. DAVIES, E. B.: Heat Kernels and Spectral Theory, Cambridge University Press, Cambridge, 1989
18. DUONG, X. T., and ROBINSON, D. W.: Semigroup Kernels, Poisson Bounds, and Holomorphic Fuctional Calculus, J. Funct. Anal. 142 (1996), 89-128
19. ELST, A. F. M. TER, and ROBINSON, D. W.: Second-Order Subelliptic Operators on Lie Groups II: Real Measurable Principal Coefficients, tech. rep., Australian National University, 1996
20. FABES, E. B., and STROOCK, D. W.: A New Proof of Moser's Parabolic Harnack Inequality Using the Old Ideas of Nash, Arch. Rational Mech. Anal. 96 (1986), 327-338
21. GILBARG, D., and TRUDINGER, N. S.:, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 2nd ed., 1983
22. HEWITT, E., and STROMBERG, K.: Real and Abstract Analysis, Springer-Verlag, Berlin, 1965
23. LADYŽENSKAJA, O. A., SOLONNIKOV, V. A., and URAL'CEVA, N. N.: Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc. Providence, Rhode Island, 1968
24. MARCUS, M., and MIZEL, V. J.: Every Superposition Operator Mapping One Sobolev Space into Another Is Continuous, J. Funct. Anal. 33 (1979), 217-229
25. MAZ'JA, V. G.: Classes of Regions and Embedding Theorems for Function Spaces, Soviet Math. Dokl. 1 (1960), 882-885
26. MAZ'JA, V. G.: Sobolev Spaces, Springer-Verlag, Berlin, 1985
27. NEČAS, J.: Les Méthodes Directes en Théorie des Équations Elliptiques, Academia, Prague, 1967
28. ∞-Contractivity of Semigroups Generated by Sectorial Forms, J. London Math. Soc. 46 (1991), 529-542
29. PROTTER, M. H., and WEINBERGER, H. F.: Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, NJ, 1967
30. ROBINSON, D. W.: Elliptic Operators on Lie Groups, Oxford University Press, Oxford, 1991
31. STEIN, E. M.: Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, New Jersey, 1970
32. VAROPOULOS, N. TH., SALOFF-COSTE, L., and COULHON, T.: Analysis and Geometry on Groups, Cambridge University Press, Cambridge, 1992