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

ISBN-10: 1461352347

ISBN-13: 9781461352341

ISBN-10: 1461507774

ISBN-13: 9781461507772

The new sequence, *International Mathematical Series* based by way of Kluwer / Plenum Publishers and the Russian writer, Tamara Rozhkovskaya is released at the same time in English and in Russian and begins with volumes devoted to the recognized Russian mathematician Professor **Olga****Aleksandrovna Ladyzhenskaya**, at the get together of her eightieth birthday.

O.A. Ladyzhenskaya graduated from the Moscow nation college. yet all through her occupation she has been heavily attached 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 conversant in the nonlinear idea of partial differential equations examining the books on quasilinear elliptic and parabolic equations written via O.A. Ladyzhenskaya with V.A. Solonnikov and N.N. Uraltseva.

Her effects and strategies at the Navier-Stokes equations, and different mathematical difficulties within the idea of viscous fluids, nonlinear partial differential equations and platforms, the regularity idea, a few instructions of computational research are popular. 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 leads to a few of the fields of arithmetic within which the implications, tools, and concepts of O.A. Ladyzhenskaya performed a primary role.

**Nonlinear difficulties in Mathematical Physics and comparable Topics***I* offers new effects from uncommon experts within the idea of partial differential equations and research. a wide a part of the cloth is dedicated to the Navier-Stokes equations, which play a tremendous position within the conception of viscous fluids. particularly, the life of a neighborhood powerful resolution (in the experience of Ladyzhenskaya) to the matter describing a few unique movement in a Navier-Stokes fluid is proven. Ladyzhenskaya's effects on axially symmetric strategies to the Navier-Stokes fluid are generalized and ideas with quick 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 attention-grabbing houses of the Stokes challenge are provided. The nonstationary Stokes challenge can also be investigated in nonconvex domain names and a few L_{p}-estimates for the first-order derivatives of strategies are bought. New ends up in the idea of absolutely nonlinear equations are awarded. a few asymptotics are derived for elliptic operators with strongly degenerated symbols. New effects also are awarded for variational difficulties hooked up with section transitions of capacity in controllable dynamical platforms, nonlocal difficulties for quasilinear parabolic equations, elliptic variational issues of nonstandard development, and a few enough stipulations for the regularity of lateral boundary.

Additionally, new effects are awarded on region formulation, estimates for eigenvalues on the subject of the weighted Laplacian on Metric graph, software of the direct Lyapunov approach in continuum mechanics, singular perturbation estate of capillary surfaces, partly 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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**Additional info for Nonlinear Problems in Mathematical Physics and Related Topics I: In Honor of Professor O. A. Ladyzhenskaya**

**Sample text**

0 n? Let us give a very elementary but amusing application. For any integer 2 we set fn : B{O, 1) ~ C, fn{z) = Z + Z" In. Area Formulas for u-Harmonic Mappings It is easy to check that In 17 are univalent harmonic mappings. Hence Ifn(B(O, 1))1 = jldetDfnl= j(18zfI2_lfJdI2) = j(1_l z ln-l)= n:1 1r. 2 in a special but interesting case. Assume that E LUX' (R2, Mk) and, in addition, det U takes only two distinct values, say, di and d~. , proportional to the identity) at any point, then we come back to the two-phase problem described in Sec.

From the monotonicity (and the obvious continuity) of the total mass of distribution with density pc regarded as a function of c, which has been proved, it follows that for any value I of the total mass (located between the value of the integral of rdNx and that of RdNx over M) there exists a unique value of the constant c (between the maximum and minimum of the goal function) such that the total mass of the distribution of density pc is equal to I. Thereby we have found a monotonically decreasing function I(c) = J Pc (x)dNx M and its inverse c(I) which is also a monotone function.

49. J. Keller, A theorem on the conductIVity of a composite medIUm, J. Math. Phys. 5 (1964), 548-549. 50. A. M. Dykhne, ConductIVity of a two dimensional two-phase system, Soviet Physics JETP. 32 (1971), 63-65. 51. K. S. Mendelson, EffectIVe conductivity of a two-phase material with cylmdrlcal phase boundarzes, J. AppL Phys. 46 (1975), p. 917. 52. K. A. Lurie and A. V. I. Optimization Theory AppL 42 (2) (1984), 283-304. 53. G. Francfort and F. Murat, Optimal bounds for conduction m two-dimensIOnal, two phase, amsotroplc media, Non-Classical Continuum Mechanics, Lond.

### Nonlinear Problems in Mathematical Physics and Related Topics I: In Honor of Professor O. A. Ladyzhenskaya by Giovanni Alessandrini, Vincenzo Nesi (auth.), Michael Sh. Birman, Stefan Hildebrandt, Vsevolod A. Solonnikov, Nina N. Uraltseva (eds.)

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