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Hölder-estimates for non-autonomous parabolic problems with rough data
A matrix-valued generator $\mathcal{A}$ with strong boundary coupling: A critical subspace of $D((-\mathcal{A})^{\frac{1}{2}})$ and $D((-\mathcal{A}^*)^{\frac{1}{2}})$ and implications
1. | Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, United States |
References:
[1] |
C. Baiocchi, Un teorema di interpolazione: Applicazioni ai problemi ai limiti per le equazioni a derivate parziali,, Ann. Mat. Pura Appl., 73 (1966), 233.
doi: 10.1007/BF02415089. |
[2] |
A. Bensoussan, G. Da Prato, M. Delfour and S. Mitter, Representation and Control of Infinite Dimensional Systems,, $2^{nd}$ edition, (2007).
doi: 10.1007/978-0-8176-4581-6. |
[3] |
S. Chen and R. Triggiani, Proof of two conjectures of G. Chen and D. L. Russell on structural damping for elastic systems: The case $\alpha = 1/2$,, Springer-Verlag Lecture Notes in Mathematics, 1354 (1988), 234.
doi: 10.1007/BFb0089601. |
[4] |
S. Chen and R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems: The case $1/2 \leq \alpha \leq 1$),, Pacific J. Math., 136 (1989), 15.
doi: 10.2140/pjm.1989.136.15. |
[5] |
S. Chen and R. Triggiani, Characterization of domains of fractional powers of certain operators arising in elastic systems, and applications,, J. Diff. Eqns., 88 (1990), 279.
doi: 10.1016/0022-0396(90)90100-4. |
[6] |
L. De Simon, Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine,, Rendiconti del Seminario Matematico della Universita di Padova, 34 (1964), 205.
|
[7] |
D. Fujiwara, Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order,, Proc. Japan Acad., 43 (1967), 82.
doi: 10.3792/pja/1195521686. |
[8] |
P. Grisvard, Characterization de qualques espaces d' interpolation,, Arch. Pat. Mech. Anal., 25 (1967), 40.
doi: 10.1007/BF00281421. |
[9] |
T. Kato, Fractional powers of dissipative operators,, J. Math. Soc. Japan., 13 (1961), 246.
doi: 10.2969/jmsj/01330246. |
[10] |
I. Lasiecka, Unified theory for abstract parabolic boundary problems-a semigroup approach,, Appl. Math. & Optimiz., 6 (1980), 287.
doi: 10.1007/BF01442900. |
[11] |
I. Lasiecka and R. Triggiani, Control Theory for Partial Differential Equations: Continuous and Approximation Theories I, Abstract Parabolic Systems, Encyclopedia of Mathematics and Its Applications Series, (2000).
|
[12] |
I. Lasiecka and R. Triggiani, Domains of fractional powers of matrix-valued Operators: A general approach,, Operator Semigroups Meet Complex Analysis, 250 (2015), 297.
doi: 10.1007/978-3-319-18494-4_20. |
[13] |
I. Lasiecka and R. Triggiani, Heat-structure interaction with viscoelastic damping: Analyticity with sharp analytic sector, exponential decay,, Communications on Pure & Applied Analysis, (). Google Scholar |
[14] |
C. Lebiedzik and R. Triggaini, The optimal interior regularity for the critical case of a clamped thermoelastic system with point control revisited,, Modern Aspects of the Theory of PDEs. Vol. 216 of Operator Theory: Advances and Applications, (2011), 243.
doi: 10.1007/978-3-0348-0069-3_14. |
[15] |
J. L. Lions, Especes d'interpolation et domaines de puissances fractionnaires d'openateurs,, J. Math Soc., 14 (1962), 233.
doi: 10.2969/jmsj/01420233. |
[16] |
J. L. Lions and E. Magenes, Nonhomogeneous Boundary Value Propblems and Applications, Vol. I,, Springer-Verlag (1972), (1972). Google Scholar |
[17] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, Springer Verlag, (1983).
doi: 10.1007/978-1-4612-5561-1. |
[18] |
R. Triggiani, A heat-viscoelastic structure interaction model with Neumann or Dirichlet boundary control at the interface: optimal regularity, control theoretic implications,, Applied Mathematics and Optimization, (). Google Scholar |
show all references
References:
[1] |
C. Baiocchi, Un teorema di interpolazione: Applicazioni ai problemi ai limiti per le equazioni a derivate parziali,, Ann. Mat. Pura Appl., 73 (1966), 233.
doi: 10.1007/BF02415089. |
[2] |
A. Bensoussan, G. Da Prato, M. Delfour and S. Mitter, Representation and Control of Infinite Dimensional Systems,, $2^{nd}$ edition, (2007).
doi: 10.1007/978-0-8176-4581-6. |
[3] |
S. Chen and R. Triggiani, Proof of two conjectures of G. Chen and D. L. Russell on structural damping for elastic systems: The case $\alpha = 1/2$,, Springer-Verlag Lecture Notes in Mathematics, 1354 (1988), 234.
doi: 10.1007/BFb0089601. |
[4] |
S. Chen and R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems: The case $1/2 \leq \alpha \leq 1$),, Pacific J. Math., 136 (1989), 15.
doi: 10.2140/pjm.1989.136.15. |
[5] |
S. Chen and R. Triggiani, Characterization of domains of fractional powers of certain operators arising in elastic systems, and applications,, J. Diff. Eqns., 88 (1990), 279.
doi: 10.1016/0022-0396(90)90100-4. |
[6] |
L. De Simon, Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine,, Rendiconti del Seminario Matematico della Universita di Padova, 34 (1964), 205.
|
[7] |
D. Fujiwara, Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order,, Proc. Japan Acad., 43 (1967), 82.
doi: 10.3792/pja/1195521686. |
[8] |
P. Grisvard, Characterization de qualques espaces d' interpolation,, Arch. Pat. Mech. Anal., 25 (1967), 40.
doi: 10.1007/BF00281421. |
[9] |
T. Kato, Fractional powers of dissipative operators,, J. Math. Soc. Japan., 13 (1961), 246.
doi: 10.2969/jmsj/01330246. |
[10] |
I. Lasiecka, Unified theory for abstract parabolic boundary problems-a semigroup approach,, Appl. Math. & Optimiz., 6 (1980), 287.
doi: 10.1007/BF01442900. |
[11] |
I. Lasiecka and R. Triggiani, Control Theory for Partial Differential Equations: Continuous and Approximation Theories I, Abstract Parabolic Systems, Encyclopedia of Mathematics and Its Applications Series, (2000).
|
[12] |
I. Lasiecka and R. Triggiani, Domains of fractional powers of matrix-valued Operators: A general approach,, Operator Semigroups Meet Complex Analysis, 250 (2015), 297.
doi: 10.1007/978-3-319-18494-4_20. |
[13] |
I. Lasiecka and R. Triggiani, Heat-structure interaction with viscoelastic damping: Analyticity with sharp analytic sector, exponential decay,, Communications on Pure & Applied Analysis, (). Google Scholar |
[14] |
C. Lebiedzik and R. Triggaini, The optimal interior regularity for the critical case of a clamped thermoelastic system with point control revisited,, Modern Aspects of the Theory of PDEs. Vol. 216 of Operator Theory: Advances and Applications, (2011), 243.
doi: 10.1007/978-3-0348-0069-3_14. |
[15] |
J. L. Lions, Especes d'interpolation et domaines de puissances fractionnaires d'openateurs,, J. Math Soc., 14 (1962), 233.
doi: 10.2969/jmsj/01420233. |
[16] |
J. L. Lions and E. Magenes, Nonhomogeneous Boundary Value Propblems and Applications, Vol. I,, Springer-Verlag (1972), (1972). Google Scholar |
[17] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, Springer Verlag, (1983).
doi: 10.1007/978-1-4612-5561-1. |
[18] |
R. Triggiani, A heat-viscoelastic structure interaction model with Neumann or Dirichlet boundary control at the interface: optimal regularity, control theoretic implications,, Applied Mathematics and Optimization, (). Google Scholar |
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