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Kernel analysis of elliptic partial differential equations

S. G. Hahn, E. V. Hankam
1966 IBM Systems Journal  
is multiplied by the number of unknown functions.  ...  ACKNOWLEDGMENT The authors wish to express their appreciation to Kurt Spielberg, who introduced us to this type of kernel analysis, and to MichaeI  ...  The area we have chosen for this analysis is the numerical solution of partial differential equations, since they cover applications in a great variety of problems arising in physics, chemistry, etc.  ... 
doi:10.1147/sj.54.0248 fatcat:r646lfll25cmze65hkcf5nurd4

Page 4228 of Mathematical Reviews Vol. , Issue 97G [page]

1997 Mathematical Reviews  
partial differential equations.  ...  |Wood, David Harlan] (1-DE-C; Newark, DE) Solving elliptic partial differential equations with MACSYMA.  ... 

Page 497 of Mathematical Reviews Vol. , Issue 2004a [page]

2004 Mathematical Reviews  
Properties of frequency compo- nents of the solution to partial differential equations at the basis of this approach are investigated in Section 2.  ...  differential equations.  ... 

Page 5357 of Mathematical Reviews Vol. , Issue 96i [page]

1996 Mathematical Reviews  
Zhevandrov (MEX-MICM; Morelia) Partial differential equations of elliptic type 96i:35023 961:35020 35330 35B99 Davies, E. B. (4-LNDKC; London) Heat kernel bounds for higher order elliptic operators.  ...  H6rmander, The analysis of linear partial differential operators. IIT, Springer, Berlin, 1985; MR 87d:35002a].  ... 

Page 1954 of Mathematical Reviews Vol. , Issue 83e [page]

1983 Mathematical Reviews  
Salle) Wallner, Herbert 83e:35026 A note on a paper concerning the construction of integral operators: ‘*Construction of kernels of integral operators for linear partial differential equations” [Applicable  ...  The paper coutains a survey of results in the function-theoretic approach to the theory of partial differential equations by means of integral operators of Bergman type.  ... 

Page 4386 of Mathematical Reviews Vol. , Issue 89H [page]

1989 Mathematical Reviews  
The author studies the Neumann boundary value problem for 35 PARTIAL DIFFERENTIAL EQUATIONS 4386 selfadjoint systems, elliptic in the sense of Douglis-Nirenberg in a domain in Euclidean n-space with an  ...  From the introduction:“Existence and symmetry properties of so- lutions are among the major questions in the study of partial differential equations.  ... 

Page 5947 of Mathematical Reviews Vol. , Issue 95j [page]

1995 Mathematical Reviews  
Summary: “We consider the solution of the elliptic partial differ- ential equation in an unbounded domain.  ...  Some examples of the usefulness of these functions in the solution of partial differential equations for nonscalar fields are given.” {Part I has been reviewed [MR 92j:35023].}  ... 

Page 6217 of Mathematical Reviews Vol. , Issue 96j [page]

1996 Mathematical Reviews  
partial differential equations.  ...  Methods Partial Differential Equations 12 (1996), no. 2, 147-159.  ... 

Page 229 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
229 35J Partial differential equations of elliptic type 99a:35029 35HOS 22E25 35)30 47F0S ter Elst, A. F. M.  ...  -Verein. 99 (1997), no. 4, 149-163. in this nice survey paper the author discusses some of the con- nections between the study of partial differential equations and noncommutative harmonic analysis.  ... 

Partial Differential Equations and Function Spaces

Shijun Zheng, Simone Secchi, Huoxiong Wu, Nguyen Cong Phuc
2016 Journal of Function Spaces  
Wu et al. establishes the nonexistence of solutions to a semilinear elliptic equation with unbounded inhomogeneous power nonlinearity.  ...  This is a Liouville type theorem that has proven to be a powerful tool in obtaining a priori bound for solutions of elliptic equations. The paper by J. Cunanan and Y.  ...  Without the significant contributions made by these researchers, the publication of the special issue would not be possible.  ... 
doi:10.1155/2016/3085105 fatcat:xm2msllpmjc7dl7sbidqekxlvu

CONTENTS [chapter]

1976 Introduction to Partial Differential Equations  
Fourier Analysis of the Wave Operator 177 E. The Wave Equation in Bounded Domains 183 F. The Radon Transform 185 Chapter 6 THE L 2 THEORY OF DERIVATIVES 190 A. Sobolev Spaces on M" 190 B.  ...  Solution of the Problems 134 F. Further Remarks 139 Chapter 4 THE HEAT OPERATOR 142 A. The Gaussian Kernel 143 B. Functions of the Laplacian 149 C.  ... 
doi:10.1515/9780691213033-toc fatcat:rssl33xip5c6dg3wyy3iyapykq

Page 580 of Mathematical Reviews Vol. , Issue 83b [page]

1983 Mathematical Reviews  
These papers are part of the author’s study of elliptic partial differential equations. He studies convolutions with kernels which he calls of class UD.  ...  Bernhard Kawohl (Erlangen) Bailet-Intissar, Joélle 83b:35036 Nonlinear mixed boundary value problems for elliptic partial differential equations. Proc. Roy. Soc. Edinburgh Sect.  ... 

Page 142 of Mathematical Reviews Vol. 49, Issue 1 [page]

1975 Mathematical Reviews  
Bergman, Integral operators in the theory of linear partial differential equations, Ergeb. Math. Grenzgeb.  ...  Bergman [Integral operators in the theory of linear partial differential equations, Ergeb. Math. Grenzgeb.  ... 

Page 7521 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
7521 35J Partial differential equations of elliptic type operator in this class.  ...  Vladimir Tulovsky (1-STJ2-MS; Staten Island, NY) 35J Partial differential equations of elliptic type 97m:35041 35J05 30E10 45E10 65N15 73D25 76Q05 Abrahams, I.  ... 

Page 426 of Mathematical Reviews Vol. , Issue 92a [page]

1992 Mathematical Reviews  
Summary: “Integral equations in a class 4, whose kernels are kernels of positive rational functions of elliptic operators, do not in general have locally integrable solutions.  ...  Summary: “An explicit and computable scheme is given for mixed coupled partial difference systems appearing when one considers difference approximate solutions of coupled systems of partial differential  ... 
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