A-priori estimates of Carleman's type in domains with boundary Journal des Mathematiques Pures et Appliquees, 73 (1994) 355-387.; Unique continuation for P.D.E's: between Holmgren's theorem and Hormander's theorem, Communications in Partial Differential Equations, 20 (1995), 855-884

A TRIBUTE TO LARS HORMANDER¨ NICOLAS LERNER Lars Hormander, 1931–2012¨ Contents Foreword 1 Before the Fields Medal 2 From the ﬁrst PDE book to the four-volume treatise 4 Writing the four-volume book, 1979-1984 9 Intermission Mittag-Leﬄer 1984-1986, back to Lund 1986 13 Students 15 Retirement in 1996 15 Final comments 15 References 16

work on PDE, in particular his characterization of. Receiving the Fields Medal from King Gustav VI. Adolf. Opening ceremony of ICM in Stockholm, 1962. From left: Lars Gårding, Lars Hörmander, John. I'm having a bit of problem filling in the gap for Theorem 5.2.6. in Hormander's first volume on linear PDE. It says that if $\kappa \in \mathcal{C}^{\infty}(X_1 \times X_2)$ is a smooth function t to PDE; typically harmonic analysis is only used to control the PDE locally, and other methods (e.g. using conserved integrals of motion) are then used to extend this control globally.

. . . . . .

So, we have Hormander's book.

THE HORMANDER CONDITION FOR DELAYED STOCHASTIC¨ DIFFERENTIAL EQUATIONS REDA CHHAIBI AND IBRAHIM EKREN Abstract. In this paper, we are interested in path-dependent stochastic diﬀerential equations (SDEs) which are controlled by Brownian motion and its delays. Within this non-Markovian context, we give a Ho¨rmander-type criterion for the

Opening ceremony of ICM in Stockholm, 1962. From left: Lars Gårding, Lars Hörmander, John. Regularity for the minimum time function with Hormander vector ﬁelds¨ Piermarco Cannarsa University of Rome “Tor Vergata” VII PARTIAL DIFFERENTIAL EQUATIONS, OPTIMAL DESIGN A-priori estimates of Carleman's type in domains with boundary Journal des Mathematiques Pures et Appliquees, 73 (1994) 355-387.; Unique continuation for P.D.E's: between Holmgren's theorem and Hormander's theorem, Communications in Partial Differential Equations, 20 (1995), 855-884 PDE on the product of the state space of the model and the space of probability measures on the state space. This PDE, typically in infinite dimensions, was touted by Lions as the proper tool to characterize equilibria.

Minnesdag för Lars Hörmander, Lund 2 februari 2013. Personligt anförande utan with PDE approach”, KTH, 16 december 2013. Sergei Merkulov. • Member of

From left: Lars Gårding, Lars Hörmander, John. I'm having a bit of problem filling in the gap for Theorem 5.2.6. in Hormander's first volume on linear PDE. It says that if $\kappa \in \mathcal{C}^{\infty}(X_1 \times X_2)$ is a smooth function t to PDE; typically harmonic analysis is only used to control the PDE locally, and other methods (e.g. using conserved integrals of motion) are then used to extend this control globally. Related to this emphasis on local phenomena is the wide-spread use in harmonic analysis of cutoﬀ functions - smooth, compactly supported Unique continuation for pde's.

A Calderon-Zygmund operator is an operator given by the formal expression Tf(x) := lim "!0 Z Rn ˜ jx yj>"K(x y)f(y)dy; where Kis a Calderon-Zygmund operator. That this is indeed a well-de ned operator, at least when f 2 S(Rn), follows from Lemma 1.3. provide examples non linear Hormander type PDE (see [39, 84]).¨ We also notice that the fundamental solution of a Kolmogorov equation has a natural interpretation in probability theory, (see for example [90]).
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On March 17-19 and May 19-21,1995, analysis seminars were organized jointly at the universities of Copenhagen and Lund, under the heading "Danish-Swedish Analysis Seminar". The main topic was partial differen- tial equations and related problems of mathematical physics. The lectures given are presented in this volume, some as short abstracts and some as quite complete expositions or survey I'm having a bit of problem filling in the gap for Theorem 5.2.6. in Hormander's first volume on linear PDE. It says that if $\kappa \in \mathcal{C}^{\infty}(X_1 \times X_2)$ is a smooth function t In some sense, the space of all possible linear PDE's can be viewed as a singular algebraic variety, where Hormander's theory applies only to generic (smooth) points and the most interesting and heavily studied PDE's all lie in a lower-dimensional subvariety and mostly in the singular set of the variety.

Solvability results for a linear PDE Au= fcan often be ob-tained by duality from uniqueness results for the adjoint equa-tion Au= 0. Similarly, controllability results for a linear PDE Au= 0 are often equivalent with certain uniqueness results for the adjoint equation. Optimal stability results for the Cauchy problem for elliptic An introduction to Gevrey Spaces. Fernando de Ávila Silva Federal University of Paraná - Brazil Seminars on PDE’s and Analysis (UFPR-BRAZIL) April 2017 - Curitiba 1 / 25
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algebra, number theory and subsequently partial differential equations. in 1952 Hörmander began working on the theory of partial differential equations.

This in turn leads to an a regularity theorem for a compactly supported distributional solution on a bounded open domain. BOOK REVIEWS 161 6. , 9, Masson, Paris, New York, Barcelona, Milan, Mexico, Rio de Janeiro, 1982. 7. Jean Dieudonné, Orientation générale des mathématiques pures N2 - We obtain microlocal analogues of results by L. Hormander about inclusion relations between the ranges of first order differential operators with coefficients in C-infinity that fail to be locally solvable.

Nirenberg and Hormander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also

Hormander L. 1994, The Analysis of Linear Partial Differential Operators 4: Fourier Integral Operators, Springer. Sobolev S. 1989, Partial Differential Equations of Mathematical Physics, Dover, New York.

Chapter VII of [Hor66] already derives a deep existence theorem for solutions of PDE equations with constant coeﬃcients. More surprisingly, there are also striking appli-cations in number theory.