By Giovanni Alessandrini, Vincenzo Nesi (auth.), Michael Sh. Birman, Stefan Hildebrandt, Vsevolod A. Solonnikov, Nina N. Uraltseva (eds.)

The new sequence, *International Mathematical Series* based through Kluwer / Plenum Publishers and the Russian writer, Tamara Rozhkovskaya is released concurrently in English and in Russian and starts off with volumes devoted to the well-known Russian mathematician Professor **Olga****Aleksandrovna Ladyzhenskaya**, at the celebration of her eightieth birthday.

O.A. Ladyzhenskaya graduated from the Moscow kingdom college. yet all through her occupation she has been heavily hooked up with St. Petersburg the place she works on the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences.

Many generations of mathematicians became acquainted with the nonlinear thought of partial differential equations examining the books on quasilinear elliptic and parabolic equations written by means of O.A. Ladyzhenskaya with V.A. Solonnikov and N.N. Uraltseva.

Her effects and techniques at the Navier-Stokes equations, and different mathematical difficulties within the idea of viscous fluids, nonlinear partial differential equations and structures, the regularity concept, a few instructions of computational research are renowned. So it truly is no shock that those volumes attracted best experts in partial differential equations and mathematical physics from greater than 15 international locations, who current their new ends up in a number of the fields of arithmetic during which the implications, equipment, and concepts of O.A. Ladyzhenskaya performed a basic role.

**Nonlinear difficulties in Mathematical Physics and comparable Topics***I* offers new effects from distinctive experts within the concept of partial differential equations and research. a wide a part of the cloth is dedicated to the Navier-Stokes equations, which play an immense function within the conception of viscous fluids. specifically, the lifestyles of a neighborhood powerful resolution (in the feel of Ladyzhenskaya) to the matter describing a few detailed movement in a Navier-Stokes fluid is verified. Ladyzhenskaya's effects on axially symmetric ideas to the Navier-Stokes fluid are generalized and strategies with quickly decay of nonstationary Navier-Stokes equations within the half-space are acknowledged. software of the Fourier-analysis to the examine of the Stokes wave challenge and a few fascinating homes of the Stokes challenge are awarded. The nonstationary Stokes challenge can be investigated in nonconvex domain names and a few L_{p}-estimates for the first-order derivatives of options are got. New ends up in the idea of totally nonlinear equations are provided. a few asymptotics are derived for elliptic operators with strongly degenerated symbols. New effects also are offered for variational difficulties hooked up with part transitions of ability in controllable dynamical structures, nonlocal difficulties for quasilinear parabolic equations, elliptic variational issues of nonstandard progress, and a few adequate stipulations for the regularity of lateral boundary.

Additionally, new effects are awarded on quarter formulation, estimates for eigenvalues in relation to the weighted Laplacian on Metric graph, software of the direct Lyapunov procedure in continuum mechanics, singular perturbation estate of capillary surfaces, in part unfastened boundary challenge for parametric double integrals.

**Read Online or Download Nonlinear Problems in Mathematical Physics and Related Topics I: In Honor of Professor O. A. Ladyzhenskaya PDF**

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**Extra resources for Nonlinear Problems in Mathematical Physics and Related Topics I: In Honor of Professor O. A. Ladyzhenskaya**

**Sample text**

1957), no. 43, 451-503. 10. 1. Bers and L. Nirenberg, On a representatIOn theorem for lmear elltpttc systems With dlscontmuous coeffictents and tts appitcatlOns, Convegno Internazionale sulle Equazioni aile Derivate Parziali, Cremonese, Roma, 1955, pp. 111-138. 11. L. Bers, F. John, and M. Schechter, Partwl Dtfferentlal Equations, Interscience Publishers, New York, 1964. 12. N. Meyers, An LP -estimate for the gradient of solutIOns of second order elliptiC dwergence form equatIOns, Ann. Sc. Norm.

Then, at = z(u) > R2. 5) . qo;. 2). Similarly, Rl ~ z(u). 2 follows from the strong maximum principle (cf. [12, Theorem 1]). 4. 1. Let 1 :::; m :::; n, and let 'if;(X) be a positIVe Cl-functlon In the annulus u E sn, p E [R l , R 2], 0 < Rl < R2 < a. Let z E C 3 (sn) be an admiSSible solutIOn of Eq. 6) satisfymg the mequalltles n: Rl :::; z(u) :::; R2, u E sn. F'/2(p)]:::; O. 4) Then where the constant C depends only on m, n, R 1 , R 2 , 'if;, and grad'if;. A Priori Estimates for Starshaped Hypersurfaces PROOF.

7]. 18 Giovanni Alessandrini and Vincenzo Nesi References 1. O. A. , Springer-Verlag, New York, 1985. 2. A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic AnalYSIS for PerIOdic Structures, North-Holland, Amsterdam, 1978. 3. S. Spagnolo, Sui limite delle soluzlonl dl probleml dl Cauchy relativi all'equazlOne del calore, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (3) 21 (1967), 657-699. 4. ___ , Sulla convergenza di soluzlonl dl equazlOni paraboliche ed ellttttche, Ann. Sc. Norm. Super. Pisa, Cl.